diff --git a/.ipynb_checkpoints/Getting Started - GitHub-checkpoint.ipynb b/.ipynb_checkpoints/Getting Started - GitHub-checkpoint.ipynb new file mode 100644 index 0000000..2ae7c34 --- /dev/null +++ b/.ipynb_checkpoints/Getting Started - GitHub-checkpoint.ipynb @@ -0,0 +1,127 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9d89079c", + "metadata": {}, + "source": [ + "# Getting Started with GitHub\n", + "\n", + "The first step is to download Git. Known as *the* open source version control system, Git is a software designed to help groups of people work together on the same code efficiently and effectively. To get started, if you haven't already, download git at https://git-scm.com/book/en/v2/Getting-Started-Installing-Git. Alternatively, GitHub also has a friendlier interface known as GitHub Desktop which will allow you to use Git without have to work through a terminal. https://desktop.github.com/\n", + "\n", + "\n", + "\n", + "Next you'll create a personal GitHub account which you can do at https://github.com/. Once your account is set up you can create a repository by clicking on the button that says ***New*** repositories on the website. (Note that you can also create repositories by using the Desktop app). You should then name your repository with your name and a descriptor for this class because you will be using this repository to share your codes with the instructor and the grader. e.g. John-Doe-QC-Homework. Initialize a README markdown file and feel free to add a description and choose whether to make it public or private. \n", + "
\n", + "If you choose to make it private, make sure the instructors have access as collaborators on the repository. After you press create repository, search for the settings tab within the GitHub view of your repository. The manage access page will allow you to share access to this directory with select individuals. Invite Matt (mm052118) and Kaelyn (kaelynj) so that they can view your code. \n", + "
\n", + "\n", + "***\n", + "\n", + "GitHub keeps track of your projects through a system of **commits**, a snapshot of all of the changes you've made to a project (adding/deleting files, making changes to your code, etc.) at particular points in time. Once changes are committed locally on your machine, you can then **push** your commit to your github repository where those changes will be stored online.\n", + "\n", + "Test out this process by first cloning your new repository to your machine, making some changes to the README.md file and creating a commit using either the command line or desktop app.\n" + ] + }, + { + "cell_type": "markdown", + "id": "235e7035", + "metadata": {}, + "source": [ + "First clone your repository in the desktop app from the lefthand menu *Current Repository* and click *Add* where you'll be prompted to specify the repo either through your account or by a specific url. On the terminal the command to clone is:\n", + "\n", + "``$~ git clone https://your/repo/url/here``" + ] + }, + { + "cell_type": "markdown", + "id": "64fd51f0", + "metadata": {}, + "source": [ + "![Step 1](./img/GithubDesktop-Step1.png)" + ] + }, + { + "cell_type": "markdown", + "id": "50b71926", + "metadata": {}, + "source": [ + "Next make some changes to your README.md file and commit them with a commit message describing the changes you've made. On the terminal you can commit the whole project directory via:\n", + "\n", + "```$~ git add *```\n", + "\n", + "```$~ git commit```" + ] + }, + { + "cell_type": "markdown", + "id": "e81765ae", + "metadata": {}, + "source": [ + "![Step 2](./img/GithubDesktop-Step2.PNG)" + ] + }, + { + "cell_type": "markdown", + "id": "3e8b02ba", + "metadata": {}, + "source": [ + "Now that you have commited the changes, you can then push them to the remote repository which lives on your github profile. The terminal command for this is, perhaps unsurprisingly\n", + "\n", + "```$~ git push```" + ] + }, + { + "cell_type": "markdown", + "id": "b7237710", + "metadata": {}, + "source": [ + "![Step 3](./img/GithubDesktop-Step3.PNG)" + ] + }, + { + "cell_type": "markdown", + "id": "b44fa2e2", + "metadata": {}, + "source": [ + "Now you know the barebones essentials of how we'll be using git. To submit the lab assignments you'll need to update your repository with jupyter notebooks completing each lab by the due date.\n", + "\n", + "To get started with the labs, clone the repository here: https://github.com/kaelynj/PHYS-7403" + ] + }, + { + "cell_type": "markdown", + "id": "1a8f8e76", + "metadata": {}, + "source": [ + "***\n", + "There is also plenty more functionality to git and github which we have not covered here. Git is a powerful tool (and helpful in a pinch after you've accidentally broken your code) and has many different features including branching, pull requests, and merging, among others. We haven't gone into detail on what else you can do with git, but there are plenty of tutorials out there in case you become curious.\n", + "\n", + "https://docs.github.com/en/get-started\n", + "https://product.hubspot.com/blog/git-and-github-tutorial-for-beginners\n", + "https://learngitbranching.js.org/" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/.ipynb_checkpoints/Getting Started-checkpoint.ipynb b/.ipynb_checkpoints/Getting Started-checkpoint.ipynb new file mode 100644 index 0000000..0f36c5a --- /dev/null +++ b/.ipynb_checkpoints/Getting Started-checkpoint.ipynb @@ -0,0 +1,524 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Getting started with Qiskit\n", + "\n", + "Here, we provide an overview of working with Qiskit. \n", + "\n", + "Before we begin, let's make sure we have a working development environment\n", + "\n", + "1. **Install anaconda.** https://www.anaconda.com/products/individual

\n", + " \n", + " \n", + "2. **Install qiskit**
\n", + " In the anaconda prompt type create a new environment using the command `conda create -n qiskit python=3`. Then activate the enviroment with `conda activate qiskit`. Finally install the package with `pip install qiskit` (or pip install qiskit[visualization])

\n", + " ***NOTE TO WINDOWS USERS***\n", + "
\n", + " You may need to download some C++ libraries for windows which aren't available by default. :( If you get an error when doing pip install qiskit this could be the issue.

\n", + " 1. Download and install the visual studio installer: \n", + "https://visualstudio.microsoft.com/downloads/
\n", + " 2. Under Visual Studio Build Tools, check the Desktop development with C++ and additionally select\n", + " \n", + "
\n", + " 3. Let the installer download and install the C++ libraries you've selected\n", + "
\n", + "\n", + "\n", + "3. **Create an IBMQ account** https://quantum-computing.ibm.com/ and obtain an API token so that you can run your circuits on real IBM quantum computers.
\n", + "
\n", + "4. **Install miscellaneous packages** Install the following packages to ensure all the lab notebooks will cooperate \n", + " 1. `pip install matplotlib`\n", + " 2.`pip install pylatexenc`\n", + " 3. `pip install seaborn`\n", + " 4. `pip install ipywidgets`\n", + " 5. `pip install jupyter`\n", + " 6. `pip install qiskit-nature[pyscf]`\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Using Qiskit\n", + "\n", + "The fundamental unit you will primarily work with in Qiskit the QuantumCircuit object. The basic workflow to using Qiskit consists of two stages: build and execute. Building involves making different quantum circuits which represent the problem/algorithm you are solving. Executing takes care of the, well, *execution* of those circuits as a job or set of jobs to be run on either real or simulated hardware. After the jobs have been run, the data is collected and must be postprocessed depending on the desired output." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "configrc.store_credentials:WARNING:2022-01-17 16:53:25,772: Credentials already present. Set overwrite=True to overwrite.\n" + ] + } + ], + "source": [ + "import qiskit \n", + "from qiskit import IBMQ\n", + "import numpy as np\n", + "from qiskit import QuantumCircuit\n", + "from qiskit import Aer\n", + "from qiskit import *\n", + "\n", + "#make sure your qiskit version is up to date\n", + "qiskit.__qiskit_version__\n", + "\n", + "#Store your API token locally\n", + "IBMQ.save_account(\"TOKEN\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Building the circuit \n", + "\n", + "The basic element needed for your first program is the QuantumCircuit. We begin by creating a QuantumCircuit comprised of two qubits." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Create a Quantum Circuit acting on a quantum register of two qubits\n", + "circ = QuantumCircuit(2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then add gates to the circuit. We start with a Hadamard gate acting on qubit $0$ and then add a $C_X$ (CNOT) gate using $0$ as the control qubit and $1$ as the target. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Add a H gate on qubit 0, putting this qubit in superposition.\n", + "circ.h(0)\n", + "# Add a CX (CNOT) gate on control qubit 0 and target qubit 1, putting\n", + "# the qubits in a Bell state.\n", + "circ.cx(0, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can visualize your circuit using Qiskit QuantumCircuit.draw(), which plots the circuit in the form found in many textbooks." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "circ.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
     ┌───┐     \n",
+       "q_0: ┤ H ├──■──\n",
+       "     └───┘┌─┴─┐\n",
+       "q_1: ─────┤ X ├\n",
+       "          └───┘
" + ], + "text/plain": [ + " ┌───┐ \n", + "q_0: ┤ H ├──■──\n", + " └───┘┌─┴─┐\n", + "q_1: ─────┤ X ├\n", + " └───┘" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#One can also draw this in markdown\n", + "circ.draw()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[This tutorial](https://qiskit.org/documentation/tutorials/circuits_advanced/03_advanced_circuit_visualization.html) covers many of the circuit visualization tools that are available." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A few of the basic gates which can be added to a quantum circuit are the:\n", + "\n", + "* Pauli $X$, $Y$, $Z$ gates\n", + "* Hadamard $H$ gate\n", + "* $S$ (or $\\pi/2$) phase gate\n", + "* $T$ (or $\\pi/4$) phase gate\n", + "* Controlled-NOT (or Controlled-$X$) gate\n", + "* Controlled-$H$ gate\n", + "* CCX or Toffoli gate\n", + "\n", + "among many others. [This tutorial](https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html) walks through many more which are available and demonstrates the syntax for each gate desired." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulating a circuit and Executing on real hardware\n", + "\n", + "Qiskit circuits can be simulated or run on real IBM hardware. Below is the list of real backends avaliable with your IBM accounts. " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "ibmqfactory.load_account:WARNING:2022-01-20 16:05:32,357: Credentials are already in use. The existing account in the session will be replaced.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + " \n", + "ibmq_qasm_simulator\n", + "ibmq_armonk\n", + "ibmq_santiago\n", + "ibmq_bogota\n", + "ibmq_lima\n", + "ibmq_belem\n", + "ibmq_quito\n", + "simulator_statevector\n", + "simulator_mps\n", + "simulator_extended_stabilizer\n", + "simulator_stabilizer\n", + "ibmq_manila\n", + "\n", + " \n", + "ibmq_qasm_simulator\n", + "ibmq_armonk\n", + "ibmq_santiago\n", + "ibmq_bogota\n", + "ibmq_casablanca\n", + "ibmq_lima\n", + "ibmq_belem\n", + "ibmq_quito\n", + "simulator_statevector\n", + "simulator_mps\n", + "simulator_extended_stabilizer\n", + "simulator_stabilizer\n", + "ibmq_jakarta\n", + "ibmq_manila\n", + "ibm_lagos\n", + "ibm_perth\n", + "\n", + " \n", + "ibmq_qasm_simulator\n", + "ibmq_armonk\n", + "ibmq_santiago\n", + "ibmq_bogota\n", + "ibmq_casablanca\n", + "ibmq_lima\n", + "ibmq_belem\n", + "ibmq_quito\n", + "simulator_statevector\n", + "simulator_mps\n", + "simulator_extended_stabilizer\n", + "simulator_stabilizer\n", + "ibmq_jakarta\n", + "ibmq_manila\n", + "ibm_lagos\n", + "ibm_perth\n" + ] + } + ], + "source": [ + "IBMQ.load_account()\n", + "\n", + "\n", + "#List out all the backends avaiable from each provider you have access to\n", + "for provider in IBMQ.providers():\n", + " print('\\n',provider)\n", + " for backend in provider.backends():\n", + " print(backend.name())\n", + " \n", + "provider = IBMQ.get_provider(hub='ibm-q-education', group='ohio-uni-1', project='spring2022')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***\n", + "Simulating a circuit that involves measurement requires us to add classical registers for the measurements to be stored to." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Create the circuit\n", + "q = QuantumRegister(2)\n", + "c = ClassicalRegister(2)\n", + "\n", + "qc = QuantumCircuit(q,c)\n", + "# can also write \"qc = QuantumCircuit(2,2)\"\n", + "\n", + "#Add the hadamard and CNOT gates to the circuit\n", + "qc.h(0)\n", + "qc.cx(0, 1)\n", + "\n", + "#add measurements\n", + "qc.measure(0,0)\n", + "qc.measure(1,1)\n", + "\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try simulating the measurement of circuit from before on the 'aer_simulator'. This will simulate the quantum circuit on your local machine. (Which is useful for testing out algorithms before sending it to the real thing!) " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'00': 4164, '11': 4028}\n" + ] + } + ], + "source": [ + "#Define a backend object to run the circuit on\n", + "backend = Aer.get_backend('aer_simulator')\n", + "\n", + "#If desired, we can also use ibm's cloud-based classical computers to simulate our circuit:\n", + "#backend = provider.get_backend('ibmq_qasm_simulator')\n", + "\n", + "#Define the shots\n", + "shots = 8192\n", + "\n", + "#run the job with the run method\n", + "job = backend.run(qc, shots=shots)\n", + "\n", + "# get the results of the job\n", + "sim_results = job.result()\n", + "\n", + "\n", + "sim_counts = sim_results.get_counts(qc)\n", + "\n", + "#Raw count data is stored in the Result object as a dict\n", + "print(sim_counts)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.visualization import plot_histogram\n", + "plot_histogram(sim_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also execute this circuit on real hardware by changing the backend and transpiling to be compatible with that backend." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "#We will use the imb_lagos backend\n", + "backend = provider.get_backend('ibm_lagos')\n", + "\n", + "initial_layout = [0,1]\n", + "\n", + "qc_trans = transpile(qc, backend, initial_layout=initial_layout, optimization_level=3)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Job Status: job has successfully run\n", + "61e5e58b9710ff62c6de1108\n" + ] + } + ], + "source": [ + "#To keep track of our job, we can use the job_monitor module in qiskit\n", + "from qiskit.tools import job_monitor\n", + "\n", + "job = backend.run(qc_trans, shots=shots)\n", + "job_monitor(job)\n", + "\n", + "#We can also print the id of the job. Any job you submit to ibm's cloud services will have a unique job id. These\n", + "# job ids can also be used to download the results data of your job at a later time\n", + "#job = backend.retrieve_job('JOB_ID')\n", + "print(job.job_id())\n", + "\n", + "# get the results of the job\n", + "hardware_results = job.result()\n", + "\n", + "\n", + "hardware_counts = hardware_results.get_counts(qc_trans)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(hardware_counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see the real hardware gives probability for states 01 and 10 which are not present in the simulations. There are ways to mitigate this error which will be discussed later. For now recognize that the hardware is prone to errors." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Getting Started - GitHub.ipynb b/Getting Started - GitHub.ipynb index 045e2b2..2ae7c34 100644 --- a/Getting Started - GitHub.ipynb +++ b/Getting Started - GitHub.ipynb @@ -119,7 +119,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" + "version": "3.9.7" } }, "nbformat": 4, diff --git a/Getting Started.ipynb b/Getting Started.ipynb index 7985e0c..a72fb1d 100644 --- a/Getting Started.ipynb +++ b/Getting Started.ipynb @@ -62,6 +62,11 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": 1, + "metadata": {}, + "outputs": [], +======= "execution_count": 21, "metadata": { "slideshow": { @@ -77,8 +82,11 @@ ] } ], +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "source": [ - "import qiskit \n", + "#import sys\n", + "#sys.path.append(\"C:/Users/Tyler\")\n", + "#import qiskit\n", "from qiskit import IBMQ\n", "import numpy as np\n", "from qiskit import QuantumCircuit\n", @@ -86,10 +94,10 @@ "from qiskit import *\n", "\n", "#make sure your qiskit version is up to date\n", - "qiskit.__qiskit_version__\n", + "#qiskit.__qiskit_version__\n", "\n", "#Store your API token locally\n", - "IBMQ.save_account(\"TOKEN\")" + "IBMQ.save_account(\"d9cb0315acd61f732cd8a940c9f5c7c757d3b94e900d5ed104202b045c67653b9f4f78ed6ee73d230536e2baac05ca97aa8e89afa332f7e7dd458e166ef58e6a\",overwrite = True)" ] }, { @@ -107,6 +115,11 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": 6, + "metadata": {}, + "outputs": [], +======= "execution_count": 22, "metadata": { "slideshow": { @@ -126,6 +139,7 @@ ] } ], +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "source": [ "# Create a Quantum Circuit acting on a quantum register of two qubits\n", "circ = QuantumCircuit(2)\n", @@ -145,20 +159,32 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": 7, + "metadata": {}, +======= "execution_count": 23, "metadata": { "slideshow": { "slide_type": "subslide" } }, +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "outputs": [ { "data": { "text/plain": [ +<<<<<<< HEAD + "" + ] + }, + "execution_count": 7, +======= "" ] }, "execution_count": 23, +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "metadata": {}, "output_type": "execute_result" } @@ -184,6 +210,14 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+======= "execution_count": 24, "metadata": { "slideshow": { @@ -194,11 +228,16 @@ { "data": { "image/png": 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+>>>>>>> 8f22383029694453e329311994097149e9fe3562 "text/plain": [ "
" ] }, +<<<<<<< HEAD + "execution_count": 8, +======= "execution_count": 24, +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "metadata": {}, "output_type": "execute_result" } @@ -209,12 +248,17 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": 9, + "metadata": {}, +======= "execution_count": 25, "metadata": { "slideshow": { "slide_type": "subslide" } }, +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "outputs": [ { "data": { @@ -233,7 +277,11 @@ " └───┘" ] }, +<<<<<<< HEAD + "execution_count": 9, +======= "execution_count": 25, +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "metadata": {}, "output_type": "execute_result" } @@ -281,6 +329,12 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": 13, + "metadata": {}, + "outputs": [ + { +======= "execution_count": 26, "metadata": { "slideshow": { @@ -296,6 +350,7 @@ ] }, { +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "name": "stdout", "output_type": "stream", "text": [ @@ -314,24 +369,6 @@ "simulator_stabilizer\n", "ibmq_manila\n", "\n", - " \n", - "ibmq_qasm_simulator\n", - "ibmq_armonk\n", - "ibmq_santiago\n", - "ibmq_bogota\n", - "ibmq_casablanca\n", - "ibmq_lima\n", - "ibmq_belem\n", - "ibmq_quito\n", - "simulator_statevector\n", - "simulator_mps\n", - "simulator_extended_stabilizer\n", - "simulator_stabilizer\n", - "ibmq_jakarta\n", - "ibmq_manila\n", - "ibm_lagos\n", - "ibm_perth\n", - "\n", " \n", "ibmq_qasm_simulator\n", "ibmq_armonk\n", @@ -378,6 +415,11 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": null, + "metadata": {}, + "outputs": [], +======= "execution_count": 27, "metadata": { "slideshow": { @@ -397,6 +439,7 @@ "output_type": "execute_result" } ], +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "source": [ "#Create the circuit\n", "q = QuantumRegister(2)\n", @@ -429,6 +472,11 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": null, + "metadata": {}, + "outputs": [], +======= "execution_count": 28, "metadata": { "slideshow": { @@ -444,6 +492,7 @@ ] } ], +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "source": [ "#Define a backend object to run the circuit on\n", "backend = Aer.get_backend('aer_simulator')\n", @@ -469,13 +518,20 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": null, +======= "execution_count": 12, +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "metadata": { "scrolled": true, "slideshow": { "slide_type": "fragment" } }, +<<<<<<< HEAD + "outputs": [], +======= "outputs": [ { "data": { @@ -489,6 +545,7 @@ "output_type": "execute_result" } ], +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "source": [ "from qiskit.visualization import plot_histogram\n", "plot_histogram(sim_counts)" @@ -507,12 +564,17 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": null, + "metadata": {}, +======= "execution_count": 18, "metadata": { "slideshow": { "slide_type": "fragment" } }, +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "outputs": [], "source": [ "#We will use the imb_lagos backend\n", @@ -524,6 +586,11 @@ }, { "cell_type": "code", +<<<<<<< HEAD + "execution_count": null, + "metadata": {}, + "outputs": [], +======= "execution_count": 19, "metadata": { "slideshow": { @@ -541,6 +608,7 @@ ] } ], +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "source": [ "#To keep track of our job, we can use the job_monitor module in qiskit\n", "from qiskit.tools import job_monitor\n", @@ -564,6 +632,10 @@ { "cell_type": "code", "execution_count": null, +<<<<<<< HEAD + "metadata": {}, + "outputs": [], +======= "metadata": { "slideshow": { "slide_type": "fragment" @@ -595,6 +667,7 @@ "output_type": "execute_result" } ], +>>>>>>> 8f22383029694453e329311994097149e9fe3562 "source": [ "plot_histogram(hardware_counts)" ] @@ -628,20 +701,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": true, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": {}, - "toc_section_display": true, - "toc_window_display": false + } }, "nbformat": 4, diff --git a/Lab-1 Quantum Measurement/.ipynb_checkpoints/Lab01_QuantumMeasurement-checkpoint.ipynb b/Lab-1 Quantum Measurement/.ipynb_checkpoints/Lab01_QuantumMeasurement-checkpoint.ipynb new file mode 100644 index 0000000..658ddae --- /dev/null +++ b/Lab-1 Quantum Measurement/.ipynb_checkpoints/Lab01_QuantumMeasurement-checkpoint.ipynb @@ -0,0 +1,1179 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "tags": [ + "remove_cell" + ] + }, + "source": [ + "

Lab 1 Quantum Measurements

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Prerequisite\n", + "- [Ch.1.4 Single Qubit Gates](https://qiskit.org/textbook/ch-states/single-qubit-gates.html)\n", + "- [Ch.2.2 Multiple Qubits and Entangled States](https://qiskit.org/textbook/ch-gates/multiple-qubits-entangled-states.html)\n", + "- [Mitigating Noise on Real Quantum Computers](https://www.youtube.com/watch?v=yuDxHJOKsVA&list=PLOFEBzvs-Vvp2xg9-POLJhQwtVktlYGbY&index=8)\n", + "\n", + "\n", + "Other relevant materials\n", + "- [Feynman Lectures Ch. III - 12](https://www.feynmanlectures.caltech.edu/III_12.html)\n", + "- [Quantum Operation](https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html)\n", + "- [Interactive Bloch Sphere](https://nonhermitian.org/kaleido/stubs/kaleidoscope.interactive.bloch_sphere.html#kaleidoscope.interactive.bloch_sphere)\n", + "- [Ch.5.2 Measurement Error Mitigation](https://qiskit.org/textbook/ch-quantum-hardware/measurement-error-mitigation.html)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import *\n", + "import numpy as np\n", + "from numpy import linalg as la\n", + "from qiskit.tools.monitor import job_monitor\n", + "import qiskit.tools.jupyter\n", + "import matplotlib.pyplot as plt #needed to draw circuits" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Part 1: Measuring the state of a qubit

\n", + "\n", + "
\n", + "
\n", + "

Goal

\n", + "

Determine the Bloch components of a qubit.

\n", + "
\n", + "\n", + "Fundamental to the operation of a quantum computer is the ability to compute the Bloch components of a qubit or qubits. These components correspond to the expectation values of the Pauli operators $X, Y, Z$, and are important quantities for applications such as quantum chemistry and optimization. Unfortunately, it is impossible to simultaneously compute these values, thus requiring many executions of the same circuit. In addition, measurements are restricted to the computational basis (Z-basis) so that each Pauli needs to be rotated to the standard basis to access the x and y components. Here we verify the methods by considering the case of a random vector on the Bloch sphere." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓 1. Express the expectation values of the Pauli operators for an arbitrary qubit state $|q\\rangle$ in the computational basis.

\n", + "\n", + "The case for the expectation value of Pauli Z gate is given as an example. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the diagonal representation, also known as spectral form or orthonormal decomposition, of Pauli $Z$ gate and the relations among the Pauli gates (see [here](https://qiskit.org/textbook/ch-states/single-qubit-gates.html)), expectation values of $ X, Y, Z $ gates can be written using $ X=HZH$ and $Y = SXS^\\dagger$ as \n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\langle Z \\rangle &=\\langle q | Z | q\\rangle =\\langle q|0\\rangle\\langle 0|q\\rangle - \\langle q|1\\rangle\\langle 1|q\\rangle\n", + "=|\\langle 0 |q\\rangle|^2 - |\\langle 1 | q\\rangle|^2\\\\\\\\\n", + "\\langle X \\rangle &= \\\\\\\\\n", + "\\langle Y \\rangle &=\\\\\\\\\n", + "\\end{align}\n", + "\\\\\n", + "$$\n", + ", respectively.\n", + "\n", + "Therefore, the expectation values of the Paulis for a qubit state $|q\\rangle$ can be obtained by making a measurement in the standard basis after rotating the standard basis frame to lie along the corresponding axis. The probabilities of obtaining the two possible outcomes 0 and 1 are used to evaluate the desired expectation value as the above equations show." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

2. Measure the Bloch sphere coordinates of a qubit using the Aer simulator and plot the vector on the Bloch sphere.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓Step A. Create a qubit state using the circuit method, initialize with two random complex numbers as the parameter.

\n", + "\n", + "To learn how to use the function `initialize`, check [here](https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html#Arbitrary-initialization). (go to the `arbitrary initialization` section.)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "qc = QuantumCircuit(1, 1)\n", + "\n", + "#### your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓 Step B. Build the circuits to measure the expectation values of $X, Y, Z$ gate based on your answers to the question 1. Run the cell below to estimate the Bloch sphere coordinates of the qubit from step A using the Aer simulator.

\n", + "\n", + "The circuit for $Z$ gate measurement is given as an example." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# z measurement of qubit 0\n", + "measure_z = QuantumCircuit(1,1)\n", + "measure_z.measure(0,0)\n", + "\n", + "\n", + "\n", + "# x measurement of qubit 0\n", + "measure_x = QuantumCircuit(1,1)\n", + "#### your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "# y measurement of qubit 0\n", + "#### your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "shots = 2**14 # number of samples used for statistics\n", + "sim = Aer.get_backend('aer_simulator')\n", + "bloch_vector_measure = []\n", + "for measure_circuit in [measure_x, measure_y, measure_z]:\n", + " \n", + " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", + " circ_trans = transpile(qc.compose(measure_circuit), sim)\n", + " counts = sim.run(qc.compose(circ_trans), shots=shots).result().get_counts()\n", + "\n", + " # calculate the probabilities for each bit value\n", + " probs = {}\n", + " for output in ['0','1']:\n", + " if output in counts:\n", + " probs[output] = counts[output]/shots\n", + " else:\n", + " probs[output] = 0\n", + " \n", + " bloch_vector_measure.append( probs['0'] - probs['1'] )\n", + "\n", + "# normalizing the Bloch sphere vector\n", + "bloch_vector = bloch_vector_measure/la.norm(bloch_vector_measure)\n", + "\n", + "print('The Bloch sphere coordinates are [{0:4.3f}, {1:4.3f}, {2:4.3f}]'\n", + " .format(*bloch_vector))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Step C. Plot the vector on the Bloch sphere.

\n", + "\n", + "Note that the following cell for the interactive bloch_sphere would not run properly unless you work in [IQX](https://quantum-computing.ibm.com/login). You can either use `plot_bloch_vector` for the non-interactive version or install `kaleidoscope` by running \n", + "\n", + "```\n", + "pip install kaleidoscope\n", + "\n", + "```\n", + "in a terminal. You also need to restart your kernel after the installation. To learn more about how to use the interactive Bloch sphere, go [here](https://nonhermitian.org/kaleido/stubs/kaleidoscope.interactive.bloch_sphere.html#kaleidoscope.interactive.bloch_sphere)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from kaleidoscope.interactive import bloch_sphere\n", + "\n", + "bloch_sphere(bloch_vector, vectors_annotation=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.visualization import plot_bloch_vector\n", + "\n", + "plot_bloch_vector( bloch_vector )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Part 2: Measuring Energy

\n", + "\n", + "
\n", + "
\n", + "

Goal

\n", + "

Evaluate the energy levels of the hydrogen ground state using Aer simulator.

\n", + "
\n", + "\n", + "\n", + "The energy of a quantum system can be estimated by measuring the expectation value of its Hamiltonian, which is a Hermitian operator, through the procedure we mastered in part 1.\n", + "\n", + "The ground state of hydrogen is not defined as a single unique state but actually contains four different states due to the spins of the electron and proton. In part 2 of this lab, we evaluate the energy difference among these four states, which is from the `hyperfine splitting`, by computing the energy expectation value for the system of two spins with the Hamiltonian expressed in Pauli operators. For more information about `hyperfine structure`, see [here](https://www.feynmanlectures.caltech.edu/III_12.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the system with two qubit interaction Hamiltonian $H = A(XX+YY+ZZ)$ where $A = 1.47e^{-6} eV$ and $X, Y, Z$ are Pauli gates. Then the energy expectation value of the system can be evaluated by combining the expectation value of each term in the Hamiltonian.\n", + "In this case, $E = \\langle H\\rangle = A( \\langle XX\\rangle + \\langle YY\\rangle + \\langle ZZ\\rangle )$. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓 1. Express the expectation value of each term in the Hamiltonian for an arbitrary two qubit state $|\\psi \\rangle$ in the computational basis.

\n", + "\n", + "The case for the term $\\langle ZZ\\rangle$ is given as an example.\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\langle ZZ\\rangle &=\\langle \\psi | ZZ | \\psi\\rangle =\\langle \\psi|(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|)\\otimes(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|) |\\psi\\rangle\n", + "=|\\langle 00|\\psi\\rangle|^2 - |\\langle 01 | \\psi\\rangle|^2 - |\\langle 10 | \\psi\\rangle|^2 + |\\langle 11|\\psi\\rangle|^2\\\\\\\\\n", + "\\langle XX\\rangle &= \\\\\\\\\n", + "\\langle YY\\rangle &= \n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

2. Measure the expected energy of the system using the Aer simulator when two qubits are entangled. Regard the bell basis, four different entangled states.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓Step A. Construct the circuits to prepare four different bell states.

\n", + "\n", + "Let's label each bell state as\n", + "$$\n", + "\\begin{align}\n", + "Tri1 &= \\frac{1}{\\sqrt2} (|00\\rangle + |11\\rangle)\\\\\n", + "Tri2 &= \\frac{1}{\\sqrt2} (|00\\rangle - |11\\rangle)\\\\\n", + "Tri3 &= \\frac{1}{\\sqrt2} (|01\\rangle + |10\\rangle)\\\\\n", + "Sing &= \\frac{1}{\\sqrt2} (|10\\rangle - |01\\rangle)\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# circuit for the state Tri1\n", + "Tri1 = QuantumCircuit(2, 2)\n", + "# your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "# circuit for the state Tri2\n", + "Tri2 = QuantumCircuit(2, 2)\n", + "# your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "# circuit for the state Tri3\n", + "Tri3 = QuantumCircuit(2, 2)\n", + "# your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "# circuit for the state Sing\n", + "Sing = QuantumCircuit(2, 2)\n", + "# your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓Step B. Create the circuits to measure the expectation value of each term in the Hamiltonian based on your answer to the question 1.

" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# \n", + "measure_ZZ = QuantumCircuit(2)\n", + "measure_ZZ.measure_all()\n", + "\n", + "# \n", + "measure_XX = QuantumCircuit(2)\n", + "# your code goes here\n", + "\n", + "\n", + "\n", + "\n", + "# \n", + "measure_YY = QuantumCircuit(2)\n", + "# your code goes here\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓Step C. Execute the circuits on Aer simulator by running the cell below and evaluate the energy expectation value for each state.

" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "shots = 2**14 # number of samples used for statistics\n", + "\n", + "A = 1.47e-6 #unit of A is eV\n", + "E_sim = []\n", + "for state_init in [Tri1,Tri2,Tri3,Sing]:\n", + " Energy_meas = []\n", + " for measure_circuit in [measure_XX, measure_YY, measure_ZZ]:\n", + " \n", + " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", + " qc = state_init.compose(measure_circuit)\n", + " qc_trans = transpile(qc, sim)\n", + " counts = sim.run(qc_trans, shots=shots).result().get_counts()\n", + "\n", + " # calculate the probabilities for each computational basis\n", + " probs = {}\n", + " for output in ['00','01', '10', '11']:\n", + " if output in counts:\n", + " probs[output] = counts[output]/shots\n", + " else:\n", + " probs[output] = 0\n", + " \n", + " Energy_meas.append( probs['00'] - probs['01'] - probs['10'] + probs['11'] )\n", + " \n", + " E_sim.append(A * np.sum(np.array(Energy_meas)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Run this cell to print out your results\n", + "\n", + "print('Energy expectation value of the state Tri1 : {:.3e} eV'.format(E_sim[0]))\n", + "print('Energy expectation value of the state Tri2 : {:.3e} eV'.format(E_sim[1]))\n", + "print('Energy expectation value of the state Tri3 : {:.3e} eV'.format(E_sim[2]))\n", + "print('Energy expectation value of the state Sing : {:.3e} eV'.format(E_sim[3]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Step D. Understanding the result.

\n", + "\n", + "If you found the energy expectation values successfully, you would have obtained exactly the same value, $A (= 1.47e^{-6} eV)$, for the triplet states, $|Tri1\\rangle, |Tri2\\rangle, |Tri3\\rangle$ and one lower energy level, $-3A (= -4.41e^{-6} eV)$ for the singlet state $|Sing\\rangle$. \n", + "\n", + "What we have done here is measuring the energies of the four different spin states corresponding to the ground state of hydrogen and observed `hyperfine structure` in the energy levels caused by spin-spin coupling. This tiny energy difference between the singlet and triplet states is the reason for the famous 21-cm wavelength radiation used to map the structure of the galaxy. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the cell below, we verify the wavelength of the emission from the transition between the triplet states and singlet state. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# reduced plank constant in (eV) and the speed of light(cgs units)\n", + "hbar, c = 4.1357e-15, 3e10\n", + "\n", + "# energy difference between the triplets and singlet\n", + "E_del = abs(E_sim[0] - E_sim[3])\n", + "\n", + "# frequency associated with the energy difference\n", + "f = E_del/hbar\n", + "\n", + "# convert frequency to wavelength in (cm) \n", + "wavelength = c/f\n", + "\n", + "print('The wavelength of the radiation from the transition\\\n", + " in the hyperfine structure is : {:.1f} cm'.format(wavelength))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Part 3: Execute the circuits on Quantum Computer

\n", + "\n", + "
\n", + "
\n", + "

Goal

\n", + "

Re-run the circuits on a IBM quantum system. Perform measurement error mitigations on the result to improve the accuracy in the energy estimation.

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Step A. Run the following cells to load your account and select the backend

" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "provider = IBMQ.load_account()\n", + "#IBMQ.active_account() #make sure you've loaded/saved your account with using you API token\n", + "#provider.backends()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "#backend = provider.get_backend('qasm_simulator')\n", + "\n", + "backend = provider.get_backend('ibm_casablanca') " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Step B. Execute the circuits on the quantum system.

\n", + "\n", + "\n", + "In Lab1 when we executed multiple circuits on a real quantum system, we submitted each circuit as a separate job which produces the multiple job ids. This time, we put all the circuits in a list and execute the list of the circuits as one job. In this way, all the circuit executions can happen at once, which would possibly decrease your wait time in the queue." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓 Check the backend configuration information and error map through the widget to determine your initial_layout. The qubits on the hardware you want to use" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "# run this cell to get the backend information through the widget\n", + "backend" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "# assign your choice for the initial layout to the list variable `initial_layout`.\n", + "initial_layout = " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run the following cell to execute the circuits with the initial_layout on the backend." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "qc_all = [state_init.compose(measure_circuit) for state_init in [Tri1,Tri2,Tri3,Sing] \n", + " for measure_circuit in [measure_XX, measure_YY, measure_ZZ] ] \n", + "\n", + "shots = 8192\n", + "qc_all_trans = transpile(qc_all, backend, initial_layout=initial_layout, optimization_level=3)\n", + "job = backend.run(qc_all_trans, shots=shots)\n", + "print(job.job_id())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "# getting the results of your job\n", + "results = job.result()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "## To access the results of the completed job. Use the job id from two cells above\n", + "results = backend.retrieve_job('job_id').result()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Step C. Estimate the ground state energy levels from the results of the previous step by executing the cells below.

" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "def Energy(results, shots):\n", + " \"\"\"Compute the energy levels of the hydrogen ground state.\n", + " \n", + " Parameters:\n", + " results (obj): results, results from executing the circuits for measuring a Hamiltonian.\n", + " shots (int): shots, number of shots used for the circuit execution.\n", + " \n", + " Returns:\n", + " Energy (list): energy values of the four different hydrogen ground states\n", + " \"\"\"\n", + " E = []\n", + " A = 1.47e-6\n", + "\n", + " for ind_state in range(4):\n", + " Energy_meas = []\n", + " for ind_comp in range(3):\n", + " counts = results.get_counts(ind_state*3+ind_comp)\n", + " \n", + " # calculate the probabilities for each computational basis\n", + " probs = {}\n", + " for output in ['00','01', '10', '11']:\n", + " if output in counts:\n", + " probs[output] = counts[output]/shots\n", + " else:\n", + " probs[output] = 0\n", + " \n", + " Energy_meas.append( probs['00'] - probs['01'] - probs['10'] + probs['11'] )\n", + "\n", + " E.append(A * np.sum(np.array(Energy_meas)))\n", + " \n", + " return E" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "uses-hardware" + ] + }, + "outputs": [], + "source": [ + "E = Energy(results, shots)\n", + "\n", + "print('Energy expectation value of the state Tri1 : {:.3e} eV'.format(E[0]))\n", + "print('Energy expectation value of the state Tri2 : {:.3e} eV'.format(E[1]))\n", + "print('Energy expectation value of the state Tri3 : {:.3e} eV'.format(E[2]))\n", + "print('Energy expectation value of the state Sing : {:.3e} eV'.format(E[3]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Step D. Measurement error mitigation.

\n", + "\n", + "The results you obtained from running the circuits on the quantum system are not exact due to the noise from the various sources such as enery relaxation, dephasing, crosstalk between qubits, etc. In this step, we will alleviate the effects of the noise through the measurement error mitigation. Before we start, watch this [video](https://www.youtube.com/watch?v=yuDxHJOKsVA&list=PLOFEBzvs-Vvp2xg9-POLJhQwtVktlYGbY&index=8). " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.ignis.mitigation.measurement import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓Construct the circuits to profile the measurement errors of all basis states using the function 'complete_meas_cal'. Obtain the measurement filter object, 'meas_filter', which will be applied to the noisy results to mitigate readout (measurement) error.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For further helpful information to complete this task, check [here](https://qiskit.org/textbook/ch-quantum-hardware/measurement-error-mitigation.html) . " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# your code to create the circuits, meas_calibs, goes here\n", + "\n", + "# so i think you create a circuit that is just two quantum bits and then you see how the actual machine handles it.\n", + "qr = QuantumRegister(2)\n", + "meas_calibs, state_labels = complete_meas_cal(qr=qr, circlabel='mcal')\n", + "\n", + "for circuit in meas_calibs:\n", + " print('Circuit',circuit.name)\n", + " print(circuit)\n", + " print()\n", + "\n", + "\n", + "# execute meas_calibs on your choice of the backend\n", + "meas_calibs_trans = transpile(meas_calibs, backend, optimization_level=3)\n", + "#job = backend.run(meas_calibs_trans, backend, shots = shots) #not working bc of backend\n", + "job = backend.run(meas_calibs_trans, shots=shots)\n", + "print(job.job_id())\n", + "job_monitor(job)\n", + "cal_results = job.result()\n", + "\n", + "## To access the results of the completed job\n", + "#cal_results = backend.retrieve_job('job_id').result()\n", + "\n", + "\n", + "# your code to obtain the measurement filter object, 'meas_filter', goes here\n", + "\n", + "meas_fitter = CompleteMeasFitter(cal_results, state_labels, circlabel='mcal')\n", + "\n", + "#np.array_to_latex(meas_fitter.cal_matrix) #need to pip install array-to-latex? this doesnt work idk why\n", + "\n", + "#based on how the real quantum computer handles these results which are known. we can expect an error on the circuit\n", + "# we are interested in and correct using the filter and fitter.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "meas_filter = meas_fitter.filter\n", + "#array_to_latex(meas_fitter.cal_matrix) #need to pip install array-to-latex\n", + "\n", + "results_new = meas_filter.apply(results)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "E_new = Energy(results_new, shots)\n", + "\n", + "print('Energy expection value of the state Tri1 : {:.3e} eV'.format(E_new[0]))\n", + "print('Energy expection value of the state Tri2 : {:.3e} eV'.format(E_new[1]))\n", + "print('Energy expection value of the state Tri3 : {:.3e} eV'.format(E_new[2]))\n", + "print('Energy expection value of the state Sing : {:.3e} eV'.format(E_new[3]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Step E. Interpret the result.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓 Compute the relative errors ( or the fractional error ) of the energy values for all four states with and without measurement error mitigation.

" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# results for the energy estimation from the simulation, \n", + "# execution on a quantum system without error mitigation and\n", + "# with error mitigation in numpy array format \n", + "Energy_exact, Energy_exp_orig, Energy_exp_new = np.array(E_sim), np.array(E), np.array(E_new)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Calculate the relative errors of the energy values without error mitigation \n", + "# and assign to the numpy array variable `Err_rel_orig` of size 4\n", + "Err_rel_orig = (Energy_exact - Energy_exp_orig)/Energy_exact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Calculate the relative errors of the energy values with error mitigation \n", + "# and assign to the numpy array variable `Err_rel_new` of size 4\n", + "Err_rel_new = (Energy_exact - Energy_exp_new)/Energy_exact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.set_printoptions(precision=3)\n", + "\n", + "print('The relative errors of the energy values for four bell basis\\\n", + " without measurement error mitigation : {}'.format(Err_rel_orig))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.set_printoptions(precision=3)\n", + "\n", + "print('The relative errors of the energy values for four bell basis\\\n", + " with measurement error mitigation : {}'.format(Err_rel_new))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

📓 Compare the size of the errors before and after the measurment error mitigation and discuss about the effect of the readout error regarding the error map information of the backend that you selected.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Your answer:**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.19.1
qiskit-aer0.10.2
qiskit-ignis0.7.0
qiskit-ibmq-provider0.18.3
qiskit0.34.1
qiskit-nature0.3.0
System information
Python version3.9.7
Python compilerGCC 7.5.0
Python builddefault, Sep 16 2021 13:09:58
OSLinux
CPUs4
Memory (Gb)6.053215026855469
Thu Jan 20 15:40:45 2022 EST
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "

This code is a part of Qiskit

© Copyright IBM 2017, 2022.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.

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Lab 1 Quantum Measurements

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Lab 1 Quantum Measurements

" + "

Lab 1 Quantum Measurements

" ] }, { @@ -32,16 +41,43 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "ibmqfactory.load_account:WARNING:2022-02-23 20:44:36,090: Credentials are already in use. The existing account in the session will be replaced.\n" + ] + } + ], "source": [ - "from qiskit import *\n", + "#from Quantum_Computing import *\n", "import numpy as np\n", + "from qiskit import IBMQ\n", + "from qiskit import QuantumCircuit\n", "from numpy import linalg as la\n", "from qiskit.tools.monitor import job_monitor\n", "import qiskit.tools.jupyter\n", - "import matplotlib.pyplot as plt #needed to draw circuits" + "import matplotlib.pyplot as plt #needed to draw circuits\n", + "import importlib.util\n", + "import sys\n", + "provider = IBMQ.load_account()\n", + "\n", + "# For illustrative purposes.\n", + "#name = 'qiskit'\n", + "\n", + "#if name in sys.modules:\n", + "# print(f\"{name!r} already in sys.modules\")\n", + "#elif (spec := importlib.util.find_spec(name)) is not None:\n", + "# # If you choose to perform the actual import ...\n", + "# module = importlib.util.module_from_spec(spec)\n", + "# sys.modules[name] = module\n", + "# spec.loader.exec_module(module)\n", + "# print(f\"{name!r} has been imported\")\n", + "#else:\n", + "# print(f\"can't find the {name!r} module\")" ] }, { @@ -85,8 +121,16 @@ "\\begin{align}\n", "\\langle Z \\rangle &=\\langle q | Z | q\\rangle =\\langle q|0\\rangle\\langle 0|q\\rangle - \\langle q|1\\rangle\\langle 1|q\\rangle\n", "=|\\langle 0 |q\\rangle|^2 - |\\langle 1 | q\\rangle|^2\\\\\\\\\n", - "\\langle X \\rangle &= \\\\\\\\\n", - "\\langle Y \\rangle &=\\\\\\\\\n", + "\\langle X \\rangle &= \\langle q | HZH | q\\rangle\n", + "= \\langle q H^\\dagger | Z | Hq\\rangle \n", + "= \\langle qH^\\dagger|0\\rangle\\langle 0|Hq\\rangle - \\langle qH^\\dagger|1\\rangle\\langle 1|Hq\\rangle\n", + "= |\\langle 0 |Hq\\rangle|^2 - |\\langle 1 | Hq\\rangle|^2\\\\\\\\\n", + "\\langle Y \\rangle &= \\langle q | SXS^\\dagger | q\\rangle \n", + "=\\langle q|SHZHS^\\dagger | q\\rangle\n", + "=\\langle qS^\\dagger H^\\dagger|Z|HS^\\dagger q \\rangle\n", + "= \\langle qS^\\dagger H^\\dagger|0\\rangle \\langle 0|HS^\\dagger q\\rangle - \\langle qS^\\dagger H^\\dagger|1\\rangle\\langle 1|HS^\\dagger q\\rangle \\rightarrow\n", + "\\\\\\\\\n", + "\\langle Y \\rangle &= |\\langle 0 |HS^\\dagger q\\rangle|^2 - |\\langle 1 | HS^\\dagger q\\rangle|^2\\\\\\\\\n", "\\end{align}\n", "\\\\\n", "$$\n", @@ -113,18 +157,74 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "
     ┌──────────────────────────────────────────────┐\n",
+       "  q: ┤ Initialize(0.5604+0.80213j,0.16081+0.12916j) ├\n",
+       "     └──────────────────────────────────────────────┘\n",
+       "c: 1/════════════════════════════════════════════════\n",
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" + ], + "text/plain": [ + " ┌──────────────────────────────────────────────┐\n", + " q: ┤ Initialize(0.5604+0.80213j,0.16081+0.12916j) ├\n", + " └──────────────────────────────────────────────┘\n", + "c: 1/════════════════════════════════════════════════\n", + " " + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "qc = QuantumCircuit(1, 1)\n", + "import math\n", + "import random # Used for random vector generation\n", + "from qiskit import QuantumCircuit\n", + "from qiskit import QuantumRegister\n", + "\n", + "qc = QuantumCircuit(1,1)\n", "\n", "#### your code goes here\n", "\n", + "# Generate random numbers for real and complex parts of both vectors and normalization of first vector\n", + "r_one = random.uniform(-1,1)\n", + "c_one = random.uniform(-1,1)\n", + "r_two = random.uniform(-1,1)\n", + "c_two = random.uniform(-1,1)\n", "\n", + "# Make sure random normalization constant of first vector is not 0 or 1\n", + "a_square = 0.0\n", + "while (a_square <= 0.0):\n", + " a_square = random.uniform(0,1)\n", + " if a_square >= 1.0:\n", + " a_square = 0.0\n", + " \n", + "# Now, need to calculate normalization constant B for second vector\n", + "b_square_numerator = 1.0 - (a_square * (r_one**2 + c_one**2))\n", + "b_square_denominator = r_two**2 + c_two**2\n", + "b_square = b_square_numerator/b_square_denominator\n", "\n", + "# Create the complex numbers n_one and n_two\n", + "a = math.sqrt(a_square)\n", + "n_one = a*r_one + a*complex(0,1)*c_one\n", "\n", - "\n" + "b = math.sqrt(b_square)\n", + "n_two = b*r_two + b*complex(0,1)*c_two\n", + "\n", + "# Create the vector\n", + "desired_vector = [\n", + " n_one,\n", + " n_two\n", + "]\n", + "qc.initialize(desired_vector, 0)\n", + "\n", + "qc.draw()\n" ] }, { @@ -138,10 +238,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Bloch sphere coordinates are [0.388, -0.121, 0.914]\n" + ] + } + ], "source": [ + "from qiskit import Aer\n", + "#Aer.backends() # show available backends\n", + "\n", "# z measurement of qubit 0\n", "measure_z = QuantumCircuit(1,1)\n", "measure_z.measure(0,0)\n", @@ -151,16 +262,18 @@ "# x measurement of qubit 0\n", "measure_x = QuantumCircuit(1,1)\n", "#### your code goes here\n", - "\n", + "measure_x.h(0)\n", + "measure_x.measure(0,0)\n", "\n", "\n", "\n", "\n", "# y measurement of qubit 0\n", + "measure_y = QuantumCircuit(1,1)\n", "#### your code goes here\n", - "\n", - "\n", - "\n", + "measure_y.sdg(0)\n", + "measure_y.h(0)\n", + "measure_y.measure(0,0)\n", "\n", "\n", "shots = 2**14 # number of samples used for statistics\n", @@ -169,7 +282,7 @@ "for measure_circuit in [measure_x, measure_y, measure_z]:\n", " \n", " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", - " circ_trans = transpile(qc.compose(measure_circuit), sim)\n", + " circ_trans = qiskit.compiler.transpile(qc.compose(measure_circuit), sim)\n", " counts = sim.run(qc.compose(circ_trans), shots=shots).result().get_counts()\n", "\n", " # calculate the probabilities for each bit value\n", @@ -206,9 +319,36176 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "displayModeBar": true, + "editable": false, + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "line": { + "color": "rgba(105,41,196,1.0)", + "width": 10 + }, + "mode": "lines", + "type": "scatter3d", + "x": [ + 0, + 0.36916117495908574 + ], + "y": [ + 0, + -0.11526845626673372 + ], + "z": [ + 0, + 0.8703233240300762 + ] + }, + { + "anchor": "tip", + "colorscale": [ + [ + 0, + "#6929c4" + ], + [ + 1, + "#6929c4" + ] + ], + "opacity": 1, + "showscale": false, + "sizemode": "absolute", + 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from kaleidoscope.interactive import bloch_sphere\n", "\n", @@ -217,13 +36497,14 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "from qiskit.visualization import plot_bloch_vector\n", "\n", - "plot_bloch_vector( bloch_vector )" + "# TODO: Huge error here, thrown by something it seems that I do not have installed.\n", + "#plot_bloch_vector( bloch_vector )" ] }, { @@ -269,10 +36550,19 @@ "\n", "$$\n", "\\begin{align}\n", - "\\langle ZZ\\rangle &=\\langle \\psi | ZZ | \\psi\\rangle =\\langle \\psi|(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|)\\otimes(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|) |\\psi\\rangle\n", - "=|\\langle 00|\\psi\\rangle|^2 - |\\langle 01 | \\psi\\rangle|^2 - |\\langle 10 | \\psi\\rangle|^2 + |\\langle 11|\\psi\\rangle|^2\\\\\\\\\n", - "\\langle XX\\rangle &= \\\\\\\\\n", - "\\langle YY\\rangle &= \n", + "\\langle ZZ\\rangle &=\\langle \\psi | ZZ | \\psi\\rangle\n", + "=\\langle \\psi|(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|)\\otimes(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|) |\\psi\\rangle\n", + "=|\\langle 00|\\psi\\rangle|^2 - |\\langle 01 | \\psi\\rangle|^2 - |\\langle 10 | \\psi\\rangle|^2 + |\\langle 11|\\psi\\rangle|^2\n", + "\\\\\\\\\n", + "\\langle XX\\rangle &=\\langle \\psi| HZH HZH | \\psi\\rangle\n", + "= \\langle\\psi H^\\dagger H^\\dagger|(|0\\rangle\\langle 0| - |1\\rangle \\langle 1|) \\otimes(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|)|HH\\psi\\rangle \\rightarrow\n", + "\\\\\\\\\n", + "\\langle XX\\rangle &= |\\langle 00|HH\\psi\\rangle|^2 - |\\langle 01 | HH\\psi\\rangle|^2 - |\\langle 10 | HH\\psi\\rangle|^2 + |\\langle 11|HH\\psi\\rangle|^2\n", + "\\\\\\\\\n", + "\\langle YY\\rangle &=\\langle \\psi| SHZHS^\\dagger SHZHS^\\dagger | \\psi\\rangle\n", + "= \\langle\\psi S^\\dagger S^\\dagger H^\\dagger H^\\dagger|(|0\\rangle\\langle 0| - |1\\rangle \\langle 1|) \\otimes(|0\\rangle\\langle 0| - |1\\rangle\\langle 1|)|HHS^\\dagger S^\\dagger\\psi\\rangle \\rightarrow\n", + "\\\\\\\\\n", + "\\langle YY\\rangle &= |\\langle 00|HHS^\\dagger S^\\dagger\\psi\\rangle|^2 - |\\langle 01 | HHS^\\dagger S^\\dagger\\psi\\rangle|^2 - |\\langle 10 | HHS^\\dagger S^\\dagger\\psi\\rangle|^2 + |\\langle 11|HHS^\\dagger S^\\dagger\\psi\\rangle|^2\n", "\\end{align}\n", "$$" ] @@ -303,45 +36593,91 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "
     ┌───────────────────────────────────┐\n",
+       "q_0: ┤0                                  ├\n",
+       "     │  Initialize(0,-0.70711,0.70711,0) │\n",
+       "q_1: ┤1                                  ├\n",
+       "     └───────────────────────────────────┘\n",
+       "c: 2/═════════════════════════════════════\n",
+       "
" + ], + "text/plain": [ + " ┌───────────────────────────────────┐\n", + "q_0: ┤0 ├\n", + " │ Initialize(0,-0.70711,0.70711,0) │\n", + "q_1: ┤1 ├\n", + " └───────────────────────────────────┘\n", + "c: 2/═════════════════════════════════════\n", + " " + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# circuit for the state Tri1\n", "Tri1 = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", - "\n", - "\n", - "\n", - "\n", + "# Tri1 state vector and initialization\n", + "Tri1_vector = [\n", + " 1.0/math.sqrt(2),\n", + " 0,\n", + " 0,\n", + " 1.0/math.sqrt(2)\n", + "]\n", + "Tri1.initialize(Tri1_vector, [0,1])\n", + "Tri1.draw()\n", "\n", "# circuit for the state Tri2\n", "Tri2 = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", - "\n", - "\n", - "\n", + "# Tri2 state vector and initialization\n", + "Tri2_vector = [\n", + " 1.0/math.sqrt(2),\n", + " 0,\n", + " 0,\n", + " -1.0/math.sqrt(2)\n", + "]\n", + "Tri2.initialize(Tri2_vector, [0,1])\n", + "Tri2.draw()\n", "\n", "# circuit for the state Tri3\n", "Tri3 = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", - "\n", - "\n", - "\n", - "\n", + "# Tri3 state vector and initialization\n", + "Tri3_vector = [\n", + " 0,\n", + " 1.0/math.sqrt(2),\n", + " 1.0/math.sqrt(2),\n", + " 0\n", + "]\n", + "Tri3.initialize(Tri3_vector, [0,1])\n", + "Tri3.draw()\n", "\n", "# circuit for the state Sing\n", "Sing = QuantumCircuit(2, 2)\n", "# your code goes here\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n" + "# Sing state vector and initialization\n", + "Sing_vector = [\n", + " 0,\n", + " -1.0/math.sqrt(2),\n", + " 1.0/math.sqrt(2),\n", + " 0\n", + "]\n", + "Sing.initialize(Sing_vector, [0,1])\n", + "Sing.draw()\n" ] }, { @@ -353,7 +36689,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -364,17 +36700,18 @@ "# \n", "measure_XX = QuantumCircuit(2)\n", "# your code goes here\n", - "\n", - "\n", - "\n", + "measure_XX.h(0)\n", + "measure_XX.h(1)\n", + "measure_XX.measure_all()\n", "\n", "# \n", "measure_YY = QuantumCircuit(2)\n", "# your code goes here\n", - "\n", - "\n", - "\n", - "\n" + "measure_YY.sdg(0)\n", + "measure_YY.sdg(1)\n", + "measure_YY.h(0)\n", + "measure_YY.h(1)\n", + "measure_YY.measure_all()\n" ] }, { @@ -386,7 +36723,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -400,7 +36737,7 @@ " \n", " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", " qc = state_init.compose(measure_circuit)\n", - " qc_trans = transpile(qc, sim)\n", + " qc_trans = qiskit.compiler.transpile(qc, sim)\n", " counts = sim.run(qc_trans, shots=shots).result().get_counts()\n", "\n", " # calculate the probabilities for each computational basis\n", @@ -418,9 +36755,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Energy expectation value of the state Tri1 : 1.470e-06 eV\n", + "Energy expectation value of the state Tri2 : 1.470e-06 eV\n", + "Energy expectation value of the state Tri3 : 1.470e-06 eV\n", + "Energy expectation value of the state Sing : -4.410e-06 eV\n" + ] + } + ], "source": [ "# Run this cell to print out your results\n", "\n", @@ -450,9 +36798,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The wavelength of the radiation from the transition in the hyperfine structure is : 21.1 cm\n" + ] + } + ], "source": [ "# reduced plank constant in (eV) and the speed of light(cgs units)\n", "hbar, c = 4.1357e-15, 3e10\n", @@ -499,22 +36855,44 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "metadata": { "tags": [ "uses-hardware" ] }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[,\n", + " ,\n", + " ,\n", + " ,\n", + " ,\n", + " ,\n", + " ,\n", + " ,\n", + " ,\n", + " ,\n", + " ,\n", + " ]" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "provider = IBMQ.load_account()\n", + "#IBMQ.load_account()\n", "#IBMQ.active_account() #make sure you've loaded/saved your account with using you API token\n", - "#provider.backends()" + "provider.backends()" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "metadata": { "tags": [ "uses-hardware" @@ -524,7 +36902,7 @@ "source": [ "#backend = provider.get_backend('qasm_simulator')\n", "\n", - "backend = provider.get_backend('ibm_casablanca') " + "backend = provider.get_backend('ibmq_bogota') " ] }, { @@ -546,13 +36924,38 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "metadata": { "tags": [ "uses-hardware" ] }, - "outputs": [], + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "01f9c503479d41f78a0a0c1ad0ec46b7", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "VBox(children=(HTML(value=\"

" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# run this cell to get the backend information through the widget\n", "backend" @@ -560,7 +36963,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, "metadata": { "tags": [ "uses-hardware" @@ -569,7 +36972,7 @@ "outputs": [], "source": [ "# assign your choice for the initial layout to the list variable `initial_layout`.\n", - "initial_layout = " + "initial_layout = [0,1]" ] }, { @@ -581,26 +36984,34 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "metadata": { "tags": [ "uses-hardware" ] }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "6216e63facb5eff56dd98c31\n" + ] + } + ], "source": [ "qc_all = [state_init.compose(measure_circuit) for state_init in [Tri1,Tri2,Tri3,Sing] \n", " for measure_circuit in [measure_XX, measure_YY, measure_ZZ] ] \n", "\n", "shots = 8192\n", - "qc_all_trans = transpile(qc_all, backend, initial_layout=initial_layout, optimization_level=3)\n", + "qc_all_trans = qiskit.compiler.transpile(qc_all, backend, initial_layout=initial_layout, optimization_level=3)\n", "job = backend.run(qc_all_trans, shots=shots)\n", "print(job.job_id())" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": { "tags": [ "uses-hardware" @@ -614,7 +37025,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "metadata": { "tags": [ "uses-hardware" @@ -623,7 +37034,7 @@ "outputs": [], "source": [ "## To access the results of the completed job. Use the job id from two cells above\n", - "results = backend.retrieve_job('job_id').result()\n", + "results = backend.retrieve_job('6216e63facb5eff56dd98c31').result()\n", "\n" ] }, @@ -636,7 +37047,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "metadata": { "tags": [ "uses-hardware" @@ -679,13 +37090,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "metadata": { "tags": [ "uses-hardware" ] }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Energy expectation value of the state Tri1 : 1.125e-06 eV\n", + "Energy expectation value of the state Tri2 : 1.116e-06 eV\n", + "Energy expectation value of the state Tri3 : 1.128e-06 eV\n", + "Energy expectation value of the state Sing : -3.342e-06 eV\n" + ] + } + ], "source": [ "E = Energy(results, shots)\n", "\n", diff --git a/Lab-2 Quantum Simulation/.ipynb_checkpoints/Lab-2_Quantum-Simulation-checkpoint.ipynb b/Lab-2 Quantum Simulation/.ipynb_checkpoints/Lab-2_Quantum-Simulation-checkpoint.ipynb new file mode 100644 index 0000000..7c776da --- /dev/null +++ b/Lab-2 Quantum Simulation/.ipynb_checkpoints/Lab-2_Quantum-Simulation-checkpoint.ipynb @@ -0,0 +1,495 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "39d5c114", + "metadata": {}, + "source": [ + "# Digital Quantum Simulations\n", + "$$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}$$\n", + "$$\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}$$\n", + "$$\\newcommand{\\braket}[2]{\\left\\langle{#1}\\middle|{#2}\\right\\rangle}$$" + ] + }, + { + "cell_type": "markdown", + "id": "d25a98d0", + "metadata": {}, + "source": [ + "In this tutorial, we will introduce time evolution of quantum states and how to simulate them using the Trotter-Suzuki formalism. We then show to how to run the time evolution of a one dimensional Ising chain with three sites." + ] + }, + { + "cell_type": "markdown", + "id": "eeb53dc9", + "metadata": {}, + "source": [ + "## Contents\n", + "1. [Introduction](#introduction)\n", + "2. [Trotter-Suzuki Formalism](#ts-equation)\n", + "3. [The Heisenberg Model](#heisenberg-equation)\n", + "4. [Trotterization](#trotterization)\n", + "5. [Qiskit Implementation](#qiskit)" + ] + }, + { + "cell_type": "markdown", + "id": "6a115400", + "metadata": {}, + "source": [ + "## Introduction \n", + "\n", + "Classical simulation of physical systems typically begin by solving simple differential equations such as $\\frac{dy}{dt} = f(y)$ which, to first order, has the solution $y(t+\\Delta t)\\approx y(t)+f(y)\\Delta t$. Meanwhile in quantum mechanics, we are concerned with the solution to $-i\\hbar\\frac{d\\ket{\\psi}}{dt}=H\\ket{\\psi}$, which for a time-indepent $H$, is\n", + "$$ \\ket{\\Psi(t)} = e^{-i\\hbar Ht}\\ket{\\Psi(0)} $$\n", + "\n", + "and the simulation of a quantum system requires the ability to perform the operation above. \n", + "\n", + "In most cases, this reduces to matrix exponentiation, but proves to be very difficult on classical computers due to the exponential growth of the size of the operator as the system size/Hilbert space increases. A good attempt at a first order solution is $\\ket{\\psi(t+\\Delta t)}\\approx (I-i\\hbar H\\Delta t)\\ket{\\psi(t)}$, but this is generally not satisfactory. However, if we can exponentiate the Hamiltonian, we only need a sufficiently small time step to simulate our system\n", + "\n", + "$$ \\ket{\\psi(t+\\Delta t)}= e^{-i\\hbar H\\Delta t}\\ket{\\psi(t)} $$\n", + "\n", + "Efficient approximations to the solution of this equation are possible for Hamiltonians which carry local interactions between the system's consitutent subsystems. These classes of Hamiltonians can be written in the form\n", + "\n", + "$$ H = \\sum_k^L H_k $$\n", + "\n", + "where each $H_k$ acts locally on only a portion of the total system. For example, the terms are often just two-body interactions (such as $X_iX_j$) and one-body Hamiltonians (such as $Z_i$). For the physicists out there, both the Ising and Hubbard models (as we'll see later on) can be written in this way. The advantage of writing the Hamiltonian in this way is that although the total time evolution operator $e^{iHt}$ may be difficult to compute, it is much easier to use $e^{iH_kt}$ as it acts on a much smaller subsytem and is straightforward to approximate using quantum circuits." + ] + }, + { + "cell_type": "markdown", + "id": "5909ecb8", + "metadata": {}, + "source": [ + "## Trotter-Suzuki Formalism \n", + "\n", + "Now armed with this idea of considering the Hamiltonian as a sum over a set of smaller subsystems, we can examine what our time evolution operator looks like. It is important to note that because the subsystem terms $H_k$ do not generally commute with each other, we can anotssume the exponential of the full Hamiltonian is a product of each of the terms $H_k$ i.e.\n", + "\n", + "$$e^{-i\\hbar Ht}\\neq \\prod_k e^{-i\\hbar H_kt}.$$\n", + "\n", + "We can move past this by using the first order Trotter-Suzuki formula which asymptotically approximates the sum\n", + "\n", + "$$\n", + " e^{-iHt} = \\lim_{n\\rightarrow\\infty} \\left(\\prod_l e^{-iH_lt/n} \\right)^n.\n", + "$$\n", + "\n", + "From now on we'll set $\\hbar=1$ (sorry experimentalists!). So although we cannot exponentiate this Hamiltonian exactly, we can approximate it arbitrarily well using slices of size $1/n$. Errors aside, this is still advantageous since we are able to efficiently implement a \"difficult\" gate $U(t)=e^{-iHt}$ by breaking the original problem into smaller pieces $e^{-iH_lt/n}$ which require only a limited set of elementary gates.\n", + "\n", + "\n", + "It may also help to provide a bit of an intuitive picture of the ST decomposition. In his original paper discussing universal quantum simulators, Lloyd (S. Lloyd, Science 273, 1073) gave this example on the Trotter-Suzuki formalism:\n", + "\n", + "
The method for performing the simulation is conceptually straightforward, if mathematically involved. The goal is to get the simulator from point A to point B along a particular route. But the simulator can only be driven in certain directions--the operations that can be applied experimentally are limited--so it is usually not possible to go from point A to point B directly. But by moving the simulator first a little bit in one direction, then a little bit in another, then a little bit in another, and so on, it is possible to move from A to B. A car can only be driven forward and backward--it cannot be driven sideways. But it is still possible to parallel park. The following construction demonstrates a quantum analog of a familiar classical fact: By going forward and backing up a sufficiently small distance a large enough number of times, it is possible to parallel park in a space only $\\epsilon$ longer than the length of the care
" + ] + }, + { + "cell_type": "markdown", + "id": "d36335f6", + "metadata": {}, + "source": [ + "## The Quantum Ising Model \n", + "\n", + "The Ising model with a transverse field has the form\n", + "$$\n", + " H_{Ising} = J\\sum_i(Z_iZ_{i+1} + gX_i)\n", + "$$\n", + "where $J$ is a dimensionless coupling constant and $g$ is a similarly dimensionless constant corresponding to the strength of a transverse magnetic field.\n", + "\n", + "In this model, two of the observables that are interesting to consider are the energy $\\langle H \\rangle$ and magnetization $\\langle \\sigma_z \\rangle$. For isolated systems, the energy should be constant in time (at least in the limit of the uncertainty principle) and so we'll be mostly focused on the magnetization which is a bit more interesting here.\n", + "\n", + "The time evolution operator $U(t)$ has the form\n", + "\n", + "$$\n", + " e^{-itH} = \\exp\\left(-it\\left(J\\sum_i(Z_iZ_{i+1} + gX_i)\\right)\\right)\n", + "$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "3b10807a", + "metadata": {}, + "source": [ + "### Exact Evolution for 3 Spins\n", + "\n", + "To get started with some data we can compare our circuit results to. It turns out Qiskit has a nice set of tools we can use to produce this called `opflow` (there is also a [tutorial](https://qiskit.org/documentation/tutorials/operators/01_operator_flow.html) on this module if you are so inclined). The cells below will build the Hamiltonian and corresponding (exact) time evolution operator, then apply it onto an initial state $|101\\rangle$ and measure its expectation value for several times." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b6ff1acf", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "plt.rcParams.update({'font.size': 16})\n", + "\n", + "# Import Qubit states Zero (|0>) and One (|1>), and Pauli operators (X, Y, Z)\n", + "from qiskit.opflow import Zero, One, I, X, Y, Z\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "dda78080", + "metadata": {}, + "outputs": [], + "source": [ + "# Returns matrix representation of the non-periodic Ising model for 3 spin-1/2 particles in a line\n", + "def H_ising(J: float, g: float):\n", + " #Interactions (I is the identity matrix; X and Z are Pauli matrices; ^ is a tensor product; * multiplies a scalar)\n", + " ZZs = (Z^Z^I) + (I^Z^Z)\n", + " Xs = (X^I^I) + (I^X^I) + (I^I^X)\n", + " \n", + " H = -J*(ZZs + (g*Xs))\n", + " return H\n", + "\n", + "# Returns matrix representation of U_ising(t) for a given time t and a set of system parameters\n", + "def U_ising(t, J, g):\n", + " #Compute the Ising Hamiltonian as above\n", + " H = H_ising(J, g)\n", + " # Return the exponential of -i*t multiplied by the 3 spin Ising Hamiltonian\n", + " return (t * H).exp_i()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "5c8902af", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "U = e^(-i*-1.0 * ZZI\n", + "- 1.0 * IZZ\n", + "- 1.0 * XII\n", + "- 1.0 * IXI\n", + "- 1.0 * IIX)\n" + ] + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Define array of time points\n", + "ts = np.linspace(0, np.pi, 100)\n", + "J = 1.0\n", + "g = 1.\n", + "\n", + "# Define initial state |101>\n", + "initial_state = One^Zero^One\n", + "\n", + "#Test out U operator for time t=1.0\n", + "U = U_ising(1., J, g)\n", + "print(\"U = \",U)\n", + "\n", + "# Compute probability of remaining in |101> state over the array of time points\n", + " # The '~' gives the bra of the initial state (<101|)\n", + " # @ is short hand for matrix multiplication\n", + " # U_ising(t) is the unitary time evolution at time t\n", + " # t needs to be wrapped with float(t) to avoid a bug\n", + " # (...).eval() returns the inner product <101|U_ising(t)|101>\n", + " # np.abs(...)**2 is the modulus squared of the innner product which is the expectation value, or probability, of remaining in |110>\n", + "probs_101 = [np.abs((~initial_state @ U_ising(float(t), J, g) @ initial_state).eval())**2 for t in ts]\n", + "\n", + "# Plot evolution of |101>\n", + "plt.plot(ts, probs_101)\n", + "plt.xlabel('time (t)')\n", + "plt.ylabel(r'probability of state $|101\\rangle$')\n", + "plt.title(r'Evolution of state $|101\\rangle$ under $H_{Ising}$')\n", + "plt.grid()\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2aee84c9", + "metadata": {}, + "source": [ + "### Measuring the Magnetization\n", + "\n", + "Using opflow to measure the expectation of the total magnetization $\\langle\\sigma_z\\rangle$ can similarly be written by adding in a couple functions which will compute $\\langle\\sigma_z\\rangle$ in the computational basis. In your last lab, you learned a bit about measuring expectation values and so here we will extend this by measuring over three qubits instead of just one. Recall that the $Z$ operator has the form\n", + "$$\n", + " Z = |0\\rangle\\langle0| - |1\\rangle\\langle1|\n", + "$$\n", + "and if we want to measure $Z$ for two qubits, we have a few choices: $IZ$, $ZI$, and $ZZ$\n", + "$$\n", + " IZ = |00\\rangle\\langle00| - |01\\rangle\\langle01| + |10\\rangle\\langle10| - |11\\rangle\\langle11| \\\\\n", + " ZI = |00\\rangle\\langle00| + |01\\rangle\\langle01| - |10\\rangle\\langle10| - |11\\rangle\\langle11| \\\\\n", + " ZZ = |00\\rangle\\langle00| - |01\\rangle\\langle01| - |10\\rangle\\langle10| - |11\\rangle\\langle11|\n", + "$$\n", + "where you'll notice the first two operators are measuring $Z$ on *only* the first or second qubit while $ZZ$ measures on both. To measure the magnetization we measure $Z$ on each of the qubits in our chain $\\langle\\sigma_z\\rangle=IZ + ZI$\n", + "\n", + "To extend this to a chain of *N* qubits, we can write the operator as:\n", + "\n", + "\n", + "$$ \\langle\\sigma_z\\rangle = \\frac{1}{N}\\sum_i^{2^N}p_i\\langle c_i|\\sigma_z|c_i\\rangle = \\frac{1}{N}\\sum_i^{2^N}p_i\\left(n_i^0 - n_i^1\\right) = \\frac{1}{N}\\sum_i^{2^N}p_i\\left(N - 2n_i^1\\right) \n", + "$$\n", + "\n", + "where $|c_i\\rangle$ are each of the computational basis states, $p_i$ is the probability of measuring the *i*-th state and $n_i^0$, $n_i^1$ are the number of $0$'s and $1$'s in the bit string respectively. \n" + ] + }, + { + "cell_type": "markdown", + "id": "9265a311", + "metadata": {}, + "source": [ + "\n", + "

📓 Verify that this sum is equivalent to measuring: $\\langle ZIII...I + IZII...I + IIZ...I + ... + III...IZ \\rangle$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a8c0a2bd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Computational basis states for 3 qubits\n", + "states = [Zero^Zero^Zero, Zero^Zero^One, Zero^One^Zero, Zero^One^One, \n", + " One^Zero^Zero, One^Zero^One, One^One^Zero, One^One^One]\n", + "\n", + "#Return the number of '1's in a given bit string\n", + "def bit_sum(n):\n", + " sum = 0\n", + " for bit in n:\n", + " sum += int(bit)\n", + " return sum\n", + "\n", + "#Function to compute the magnetization from a given opflow state\n", + "def sigma_z(psi_t):\n", + " state_probs = []\n", + " for state in states:\n", + " bit_string = list(state.primitive.keys())[0]\n", + " bitsum = bit_sum(bit_string)\n", + " state_probs.append((3.-2.*bitsum) * np.abs((~state @ psi_t).eval())**2)\n", + " return sum(state_probs)/3\n", + " \n", + " \n", + "ts = np.linspace(0, np.pi, 100)\n", + "\n", + "#Define your initial state\n", + "init_state = One^Zero^One\n", + "\n", + "#Compute the magnetization at each time step\n", + "mags = [sigma_z(U_ising(float(t), J, g) @ init_state) for t in ts]\n", + "\n", + "# Plot evolution of |110>\n", + "plt.plot(ts, mags)\n", + "plt.xlabel('time (t)')\n", + "plt.ylabel(r'$\\langle\\sigma_z\\rangle$')\n", + "plt.title(r'Magnetization of State $|${}$\\rangle$'.format(list(init_state.primitive.keys())[0]))\n", + "plt.grid()\n", + "plt.show()\n", + " \n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "a5d2cbdc", + "metadata": {}, + "source": [ + "## Trotterization \n", + " \n", + "Now that we understand what about the Ising model we are interested in, let's take a look at what the time evolution operator $U(t)$ looks like as we \"Trotterize\" it. If we assume a system of three sites and open boundary conditions, the Hamiltonian can be written as\n", + "$$\n", + " H_{Ising} = J\\sum_i(Z_iZ_{i+1} + gX_i) = JZ_0Z_1 + JZ_1Z_2 + JgX_0 + JgX_1 + JgX_2.\n", + "$$\n", + "\n", + "We can then expand this out using the Trotter-Suzuki decomposition with $m$ slices\n", + "$$\n", + " U(t) = \\exp\\left(-it\\left(J\\sum_i(Z_iZ_i{i+1} + gX_i)\\right)\\right) \\\\\n", + " \\approx \\left[\\prod_i \\exp\\left(-iH_i t/m\\right)\\right]^m \\\\\n", + " = \\left[e^{-it/mJ Z_0Z_1} e^{-it/mJ Z_1Z_2} e^{-it/mJgX_0} e^{-it/mJgX_1} e^{-it/mJgX_2}\\right]^m \\\\\n", + " = \\left[e^{-i\\theta_1 Z_0Z_1} e^{-i\\theta_1 Z_1Z_2} e^{-i\\theta_2X_0} e^{-i\\theta_2X_1} e^{-i\\theta_2X_2}\\right]^m\n", + "$$\n", + "\n", + "and are left with 5 exponential operators of the form either $ZZ(\\theta)$ or $X(\\theta)$. These operators have matrix representations of:\n", + "\n", + "$$\n", + " ZZ(\\theta) = \\begin{pmatrix} e^{-i\\frac{\\theta}{2}} & 0 & 0 & 0 \\\\\n", + " 0 & e^{i\\frac{\\theta}{2}} & 0 & 0 \\\\ \n", + " 0 & 0 & e^{i\\frac{\\theta}{2}} & 0 \\\\ \n", + " 0 & 0 & 0 & e^{-i\\frac{\\theta}{2}} \\end{pmatrix} \\\\ \n", + " \\\\ \n", + " X(\\theta) = \\begin{pmatrix} \\cos\\left(\\frac{\\theta}{2}\\right) & -i\\sin\\left(\\frac{\\theta}{2}\\right) \\\\\n", + " i\\sin\\left(\\frac{\\theta}{2}\\right) & \\cos\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "694b7c54", + "metadata": {}, + "source": [ + "\n", + "

📓 Expand each of the operators of U(t) and show that they are equivalent to the rotation matrices above." + ] + }, + { + "cell_type": "markdown", + "id": "cfd683a3", + "metadata": {}, + "source": [ + "## Qiskit Implementation \n", + "\n", + "

📓 Step A. Build a circuit that will implement the operator $U(t)$ for a given target time and number of Trotter steps." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "922b5255", + "metadata": {}, + "outputs": [], + "source": [ + "#### Your code goes here\n", + "\n", + "#Conveniently enough, qiskit has both a ZZ(theta) and X(theta) gates by default. Check the docs on how to call them.\n", + "#Start by calculating the angle theta for a given time and number of steps. Then create function(s) to add on \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "50fd6e68", + "metadata": {}, + "source": [ + "

📓 Step B. Measure and plot the expectation of the state $|101\\rangle$ as shown in section 3.1. Plot this for several different numbers of Trotter steps to see how the trotterized $U(t)$ begins to converge to the true $U(t)$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c43dcd1c", + "metadata": {}, + "outputs": [], + "source": [ + "#### Your code goes here\n", + "\n", + "#Note in the example plot, the parameters J = g = 1.0\n", + "\n", + "#Recall that the results are returned as a dict object with the bitstring as keys and the number of counts as values.\n", + "# A suggestion to run this quickly is to use the Aer simulator backend. For extra points, plot the time evolution\n", + "# using a real device\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "85788677", + "metadata": {}, + "source": [ + "

📓 Step C. Write a function to process the circuit results and calculate $\\langle\\sigma_z\\rangle$. Plot this against time as shown further above" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "31597ae4", + "metadata": {}, + "outputs": [], + "source": [ + "#### Your code goes here\n", + "\n", + "#A helpful starting point here is to remember that the magnetization can be measured by examining each bitstring \n", + "# from the results.\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2a41435e", + "metadata": {}, + "source": [ + "

📓 Step D. Run these circuits on your favorite backend and plot against the simulated data." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "81c03cab", + "metadata": {}, + "outputs": [], + "source": [ + "#### Your code goes here\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": {}, + "toc_section_display": true, + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Lab-2 Quantum Simulation/Lab-2_Quantum-Simulation.ipynb b/Lab-2 Quantum Simulation/Lab-2_Quantum-Simulation.ipynb index c6bb0b7..fdf715b 100644 --- a/Lab-2 Quantum Simulation/Lab-2_Quantum-Simulation.ipynb +++ b/Lab-2 Quantum Simulation/Lab-2_Quantum-Simulation.ipynb @@ -1,9 +1,20 @@ { "cells": [ { - "cell_type": "markdown", - "id": "39d5c114", + "cell_type": "code", + "execution_count": 1, + "id": "fdf22bfe", "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (Temp/ipykernel_12160/2948130777.py, line 2)", + "output_type": "error", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"C:\\Users\\Tyler\\AppData\\Local\\Temp/ipykernel_12160/2948130777.py\"\u001b[1;36m, line \u001b[1;32m2\u001b[0m\n\u001b[1;33m $$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}$$\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n" + ] + } + ], "source": [ "# Digital Quantum Simulations\n", "$$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}$$\n", @@ -248,7 +259,20 @@ "metadata": {}, "source": [ "\n", - "

📓 Verify that this sum is equivalent to measuring: $\\langle ZIII...I + IZII...I + IIZ...I + ... + III...IZ \\rangle$" + "

📓 Verify that this sum is equivalent to measuring: $\\langle ZIII...I + IZII...I + IIZ...I + ... + III...IZ \\rangle$\n", + " \n", + "$$\n", + "\\langle ZIII...I + IZII...I + ... + II...IZ \\rangle = \\langle ZII...I \\rangle + \\langle IZII...I \\rangle + ... + \\langle II...IZ \\rangle \\\\\n", + " = \\langle \\psi | ZII...I |\\psi \\rangle + ... + \\langle \\psi | II...IZ | \\psi \\rangle \\\\\n", + "$$\n", + " \n", + " where\n", + " \n", + "$$\n", + "\\langle \\psi | ZII...I |\\psi \\rangle = \\langle \\psi | 00...0 \\rangle \\langle 00...0 | \\psi \\rangle - \\langle \\psi | 10...0 \\rangle \\langle 10...0| \\psi \\rangle - \\langle \\psi |110...0 \\rangle \\langle 110...0 | \\psi \\rangle - ... - \\langle \\psi |11...1 \\rangle \\langle 11...1| \\psi \\rangle + \\langle \\psi | 00...01 \\rangle \\langle 00...01 | \\psi \\rangle + ... + \\langle \\psi | 01...1 \\rangle \\langle 01...1 | \\psi \\rangle\n", + "$$\n", + " and thus\n", + " " ] }, { @@ -351,7 +375,37 @@ "metadata": {}, "source": [ "\n", - "

📓 Expand each of the operators of U(t) and show that they are equivalent to the rotation matrices above." + "

📓 Expand each of the operators of U(t) and show that they are equivalent to the rotation matrices above.\n", + " \n", + "$$\n", + " e^{-i\\theta_1 Z\\otimes Z} = I + \\frac{(-i\\theta_1 Z\\otimes Z)}{1!} + \\frac{(-i\\theta_1 Z\\otimes Z)^2}{2!} + \\frac{(-i\\theta_1 Z\\otimes Z)^3}{3!} + ... \\\\\n", + "$$\n", + " with\n", + "$$\n", + " (Z\\otimes Z)^{2k} = I\\quad \\forall k \\in R \\\\\n", + "$$\n", + " and\n", + "$$\n", + " (Z\\otimes Z)^{2k+1} = (Z\\otimes Z)^{2k} \\times (Z\\otimes Z) = Z\\otimes Z \\\\\n", + "$$\n", + " therefore,\n", + "$$\n", + " e^{-i\\theta_1 Z\\otimes Z} = I - i\\theta_1 Z\\otimes Z - \\frac{(\\theta_1 I)}{2!} + \\frac{(i\\theta_1 Z\\otimes Z)}{3!} + ... \\\\\n", + " = (I - \\frac{(\\theta_1 I)}{2!}) - i(\\theta_1 Z\\otimes Z - \\frac{(\\theta_1 Z\\otimes Z)}{3!})\n", + " = I cos(\\theta_1) - i Z\\otimes Zsin(\\theta_1) \\\\\n", + " = \\begin{pmatrix} cos(\\theta_1) - isin(\\theta_1) & 0 & 0 & 0 \\\\\n", + " 0 & cos(\\theta_1) + isin(\\theta_1) & 0 & 0 \\\\ \n", + " 0 & 0 & cos(\\theta_1) + isin(\\theta_1) & 0 \\\\ \n", + " 0 & 0 & 0 & cos(\\theta_1) - isin(\\theta_1) \\end{pmatrix} \\\\\n", + " = \\begin{pmatrix} e^{-i\\frac{\\theta}{2}} & 0 & 0 & 0 \\\\\n", + " 0 & e^{i\\frac{\\theta}{2}} & 0 & 0 \\\\ \n", + " 0 & 0 & e^{i\\frac{\\theta}{2}} & 0 \\\\ \n", + " 0 & 0 & 0 & e^{-i\\frac{\\theta}{2}} \\end{pmatrix} \\\\ \n", + "$$\n", + " similarly, for x we have:\n", + "$$\n", + " \n", + "$$" ] }, { @@ -366,23 +420,54 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "id": "922b5255", "metadata": {}, "outputs": [], "source": [ "#### Your code goes here\n", + "import numpy as np\n", + "import qiskit\n", + "from qiskit import QuantumCircuit\n", + "import matplotlib.pyplot as plt\n", "\n", "#Conveniently enough, qiskit has both a ZZ(theta) and X(theta) gates by default. Check the docs on how to call them.\n", "#Start by calculating the angle theta for a given time and number of steps. Then create function(s) to add on \n", "\n", + "# Define function for operating gates on the quantum circuit object\n", + "#\n", + "# params: qc - quantum circuit to gate\n", + "# params: t - time at which operation takes place\n", + "# params: J - zz coupling constant\n", + "# params: g - x interaction constant\n", + "# params: m - number of trotter steps\n", + "def U_trotter(qc, t, J, g, m):\n", + " m_steps = np.linspace(0,m,m)\n", + " theta_one = t * J / m\n", + " theta_two = theta_one * g\n", + " for i in m_steps:\n", + " qc.rx(2*theta_two,2)\n", + " qc.rx(2*theta_two,1)\n", + " qc.rx(2*theta_two,0)\n", + " qc.rzz(2*theta_one,1,2)\n", + " qc.rzz(2*theta_one,0,1)\n", + " return qc\n", + " \n", + "# quantum circuit object\n", + "qc = QuantumCircuit(3,3)\n", "\n", + "# array of time points and constants\n", + "ts = np.linspace(0, np.pi, 10)\n", + "J = 1.0\n", + "g = 1.\n", + "m = 10\n", + "t = 1\n", "\n", + "# U = U_trotter(qc,t,J,g,m)\n", + "# print(U)\n", "\n", - "\n", - "\n", - "\n", - "\n" + "qc = U_trotter(qc,t,J,g,m)\n", + "# qc.draw()\n" ] }, { @@ -395,22 +480,102 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "c43dcd1c", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "#### Your code goes here\n", + "import numpy as np\n", + "import qiskit\n", + "from qiskit import QuantumCircuit\n", + "import matplotlib.pyplot as plt\n", + "from qiskit import *\n", + "# from qiskit import Aer\n", "\n", "#Note in the example plot, the parameters J = g = 1.0\n", "\n", "#Recall that the results are returned as a dict object with the bitstring as keys and the number of counts as values.\n", "# A suggestion to run this quickly is to use the Aer simulator backend. For extra points, plot the time evolution\n", "# using a real device\n", - "\n", - "\n", - "\n", - "\n" + "initial_state_vector = [\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 1,\n", + " 0,\n", + " 0\n", + "]\n", + "\n", + "# Define function for operating gates on the quantum circuit object\n", + "#\n", + "# params: qc - quantum circuit to gate\n", + "# params: t - time at which operation takes place\n", + "# params: J - zz coupling constant\n", + "# params: g - x interaction constant\n", + "# params: m - number of trotter steps\n", + "def U_trotter(initial_state, t, J, g, m):\n", + " m_steps = np.linspace(0,m,m)\n", + " theta_one = t * J / m\n", + " theta_two = theta_one * g\n", + " for i in m_steps:\n", + " initial_state.rzz(2*theta_one,0,1)\n", + " initial_state.rzz(2*theta_one,1,2)\n", + " initial_state.rx(2*theta_two,0)\n", + " initial_state.rx(2*theta_two,1)\n", + " initial_state.rx(2*theta_two,2)\n", + " return initial_state\n", + "\n", + "# array of time points and constants\n", + "ts = np.linspace(0, np.pi, 100)\n", + "J = 1.0\n", + "g = 1.\n", + "sim = Aer.get_backend('aer_simulator')\n", + "\n", + "shots = 2**13 # number of samples used for statistics\n", + "\n", + "# Loop for all ms\n", + "m_list = [1,5,10]\n", + "for m in m_list:\n", + " time_probs = []\n", + " # Loop for all times\n", + " for t in ts:\n", + " initial_state = QuantumCircuit(3,3)\n", + " initial_state.initialize(initial_state_vector, [0,1,2])\n", + " \n", + " # Run the circuit and measure\n", + " qc = U_trotter(initial_state, t, J, g, m)\n", + " qc.measure_all(add_bits = False)\n", + "\n", + " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", + " qc_trans = qiskit.compiler.transpile(qc, sim)\n", + " counts = sim.run(qc_trans, shots=shots).result().get_counts()\n", + "\n", + " # calculate the probabilities for each computational basis\n", + " probs = {}\n", + " if '101' in counts:\n", + " probs['101'] = counts['101']/shots\n", + " time_probs.append(probs['101'])\n", + " else:\n", + " time_probs.append(0)\n", + "\n", + " plt.plot(ts, time_probs)\n", + "plt.show()" ] }, { @@ -423,18 +588,126 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "id": "31597ae4", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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9CdzWUZafrkqULS9qHB4eriMjZep8e/HY93tZuj+RjU/2IcDb9W/bPtrzEbP2zwIgpKiY7u4h1A3tRlBAGxxcfVgTt5Y1cWvIKcphUutJPNThoT+fW5SdwpvL7uP7vFN0z83jrcwivPMyOODixFpPL/pkZ9GmwQAY8gF4yvDP8tJaM+iDjSgFvz/cQ9YssDNKqV1a6/Ayt0nBF9YQk5LNgP+uZ8KNDXjulhaWb2YmQtw2vsg8ynvHvuEWz4ZMiNpMWIvbUREfgcPfuwsKzAWczDhJk5pNyiwyPxxZyOs73yQAR5SDI2fMOQC4KUc+TkqmE64w4DVoczs4yB295fH9zjie/Gk/30zsQvewWkbHEdfgcgVfOuiEVcxYHY2rk4mp/1vYpMQMC8ew+PdpvHfsGwbl5PLagXU0bjYcFfHhP4o9gIvJhaa+TS/ZohzV/E4+H/QFnj71qF+7Ha92f5Vfhv1CkHddHggKYptvMPw8FWb1hGMrwYYbM7ZuaLtgank6M3fTCaOjCCuSPnxRblFJmfy2P4H7ezXCz9PF8s2dc1maEcVLAf50927I66EdMLX2hBseKlfru11AO34a+tPfvjdv4DwmrpzI9Kw4nuk9jSH7luLy7ShwcgcHJ8svlzZ3wM1vledtViuuTibu6lKPGaujOZ6aTSN/T6MjCSuQFr4ot//+cQxPZ0cm92wIQHF6HO/ufIenA2rRPrAD7w/5Fqe+L0KPx8Bk/TaGn5sf8wbOo2nNprx06lcGBNbgo863k9x+NLQbA6GdYftMiFpq9WNXZWO71sPZ5MDnm6WVX1VIwRflciA+gxWHkpnQowE+7s6k5aUx+ddRzPdyZXT9W/is/2e4O7lXeI6arjX5evDXzO4/mzb+bZmdup2BZ9fwkEsuG3s8gDmgBSz9l2V0j7gq/l4uRLQL5sdd8aTnFhodR1iBVQq+UmqQUuqoUipGKfV0GdubKaW2KqUKlFKPW+OYwja8u/IoNd2dmHBjA85lJXDvz8PZX5zFa/49eLbXmziZnCoti1KKbsHd+LDvhywdvpRxLcexL3UfD6x9kPuCg8nNSYFVL1VanqpgQo8G5BeV8LXMmV8llLvgK6VMwMfAzUALYLRSqsVFu50DHgLeLe/xhO3YefIc64+l8nz7AlhyH1MX9iUhP41Pi30YOnCGodnqeNfh0Y6PsmrkKl7s9iJ7M2N4pHFbCiPnwakthmazJ81qe9OveQAfrz1ObKpMc2HvrNHC7wzEaK1jtdaFwEIg4sIdtNYpWuudQJEVjidsgNaad1ccpa5nCTdHPcb0jF1EOzvxfusH6HTfeqjElv3lOJmcGNVkFC/f8DJbC8/yZEhdiheMhi0fQbHMCnk1XhveGhcnBx79bi9F5hKj44hysEbBDwEunHgjvvR710UpNVkpFamUikxNTS13OFExNsWcZfuJNCbU/Zl7ayj2ODvyRs+36Rk+rUIuzJbXsLBhPN35aVY7w5ggfx7b+19emhfOrxteMjiZ7Qv0duX14a3ZF5/Bh6ujjY5T5Z3IOMGy2GUV8trW+J9Z1qDp6x4ArbWeDcwGy41X1/s6omK9sWY5fo2+5V0dT7CLJ+/2epMB9QcYHeuy7mp+Fw7KgaWxS4lxS+J8bgo/nfgJUqO4NWI+OLoYHdFmDW4dxIgOIXy0NoZeTQPoWK+m0ZGqnKhzUXy2/zP+OPUHNVxqcFPdm3B1dL3yE6+BNQp+PHDhtIihQIIVXlfYqK0n4jjt9CG1HMxMP3ueiLErcApsaXSsqzK62WhGNxsNQFFRHlN+HMxLmQep90V/2oxaADWu+4/TKu+loS3ZHnuOp3/az/JHemK6zOR44urlFuXyn23/4dfYX/F08mRC6wmMbT7W6sUerFPwdwKNlVINgDPAncAYK7yusFFvbJmJMuXxaUIqzVveDnZS7C/m5OTGe8MXMfrnCB7JTWPBnF4EjvkJgtoaHc0mebs68dwtzXngm90s3nOGkTKx2hXlFeex6cwmYs7HkJSbRFJOEiGeIdzW5DZa+rUkNj2WR9c9ysnMk0xqPYnxrcbj7fzPiQetxSpz6SilBgMfACZgntb6NaXUVACt9UylVG0gEvAGSoBsoIXWOvNyrytz6dieY2fPcNuvt9Kj0IFPUuPhoT3gHWR0rHKJPh/N2KVjqF+Qxxcp6bjduQAa9DA6lk3SWhPx8WbSsgtZ83gvXBxlzqKybE3YyuKYxayLW0decR4AtdxqEeAeQGx6LPnmfJr7Nudk5kncHN14p+c7dA7qbJVjy+Rpwmomf3MXO4r28cuZZOoNeBM6TTA6klWsPb2Wh9c+TP8iB95JPIPDbXOhxVCjY9mkzTFnuWvOdl4Y0oIJNzYwOo5NyS/O5+2db/PDsR+o4VKD/vX6M7jBYNr6t8XZZFn9LbMwk6WxS1kcvRhfN19e7vYygR6BVssgBV+Un9acXjyJiMxt9M8x8faIL6tc18fnBz/n/V3vM8XswfS4ozBsJrS9w+hYNmnsnO0cTsxk/RO98XK1jSG41qK1Zv/Z/RxOO0z/ev2p5Vbrb9sOnzvM4bTDHD13lNiMWEI9Q2nr35Zgz2De3vk2Mekx3NvqXh5s92Cl3nj4P5cr+LY3fk7Ypq0f8XHiGnD3pHPX+VWu2AOMbzme2IxYZsX8TIP67bhl8RQwF0KHu42OZnOeGNiUiI8389nGEzzWv4nRca4oNiOWyKRIknKSSM5NxsXkwphmYwirGfbnPqczT/Nr7K8sjV1KXJZlpPm7O99leOPhRDSKYFviNn6O+ZnTWacB8HTypEGNBqyJW8PimMUA+Lr6MrPfTLqHdK/8N3kVpIUvruz0NtYvHMH0QD+cs/qz44H3quwIjSJzEZP+mMTelL3co72YevIA7oPfqzJdV9Y09atdbI45y9Zn++LpYnttR3OJmfXx61kQtYBtidsAMCkT/u7+ZBRkkFecR+86veka1JUVJ1ewJ2UPCkXnoM4MaTiEZr7NWBi1kCXHl1BUYrlnNDwwnIiwCMIDwwnxDEEphdaak5knOXb+GB0DO/7tLwIjSJeOuH7ZqZyb3ZMRNR1JKwxkatOPmNa7mdGpKlRWYRbvRb7HT9E/EYQjzycl0LPV3TDgP+Bk/aFy9mpvXDrDPt7Mi0NacJ+N9eXnFuXywOoH2JW8i0D3QO5oegeDGw4m0D0QRwdH0vPT+TbqW76N+paMggwa1GhARKMIhjQc8o/+9OScZDYnbKZTYCfqeNe5xBFthxR8cX20Rn81nEdzDrHW3YOCUw+x9V9jqenhbHSySrE7eTevbn2FmIzjfJCcSl/vxjDqC/BrZHQ0mzHy0y0kZeaz7vHeONrIgucF5gIeXP0g25O283zX5xkeNhxHh7L/AsktyiUpN4kG3g2qzFKOsuKVuD5Rv7EkZQer3V0pOjuQoS06VptiD9AhsAMLb/2OVn6teD64Dqey4i2raa15DfLOGx3PJkzs0ZD483msPJxsdBQAikqKeGL9E2xN3MrLN7zMqCajLlnsAdyd3GlYo2GVKfZXIgVflM1cxPlVL/JWLT9CXJqTm3oj93Srb3SqSudicuH93u/j6OjKI41aktuwJ2x4Gz5oYyn81XwCtv4tAqnn585nG2ONjkJRSRHPbnyWtXFrebbLswwLG2Z0JJsjBV+ULfJzZurz5ChF1plhhNfzo1VIDaNTGSLIM4g3e7zJ8azTvBxcl9yJq6FRH0vhX/JQtV471+SguK97A/acTmfXqcr7qyc9P52copw/H+cX5/Po2kdZfnI5/+r4rz+nzxB/JwVf/FN+Bqc2vcX33l509R/MmdQajLuhvtGpDNU9pDv3t7ufZSeW0X3tJCbUcOLzDsPIO/AdbKzeyzyM7BiKt6sjcyqhla+15stDX9Lnhz70/aEvr29/nUNph5i2ehob4jfwfJfnGd9qfIXnsFe2N5ZKGG/TB3zgBk6OLmQl9SXASzGoVW2jUxluapupdAjowOYzm9mcsJn3zx9jXcMWfLjuNbx9G0GrEUZHNISHiyN3d6vHJ+uOE5WUSbPaFTMXzLn8czy/6Xk2ntlI79DeeDl78eOxH1kQtQCTMvF6j9cZ0nBI2U8+tgKS9kPnyeBaPf9SBRmlIy6WmcCemZ25J7Amd4RNYs6vjXisfxMe6tvY6GQ2Z/nJ5Tyz8RkammFmQhL+9y6vkjekXY303EJ6vLWWro38+OyeMgeIXLfswmy+O/odXx7+kqzCLB4Pf5zRzUajlCItL40lx5fQtGZTbgi5oewXiFoG398NJcXgVhN6PA6dJv5ziG1eOqRGQZ0uYMcXcWWUjrhqxeve4F0fD/xdfEmJ64y7s4m7u9YzOpZNGlR/EB/3/Zg4R0fuqe1HzM+Tqu1FXB93Zyb1bMgfh5PZG5duldc0l5j5ZO8nDPhxAB/s/oBmvs1YcMsCxjQf8+eoGj83P+5tde+li/3xtfDDOMsv4nt/h+AOsPI5mNEG/ngRUqIgJw1WvwoftIZ5A+Hn+6Hwr+sDFObCqa1QbP8LuUsLX/xJn43htQX9+c7bkyfav8zLC10Zf0N9Xhhy8RLF4kIHUg8w/Y/JZBdk8VjN9oyJ+LLaDPO7UHZBMT3fXkvLYG++mtClXK+ltealrS+xKHoR/er2Y2KbibT0K2Mabq1h0/sQHwnOHqUfnuDiDQ4m2Pge+DaEcb+Cu6/lObHrYftMiF5pafU7OFk+txgKNevD5v+DgOYw+F04vhoiP4e8c+BTF3o/A23usLy2jZIbr8RVmb9gMO8WxnFv49tJTx3Ogh2n2fBkH4JquBkdzeadzTvLi4tuY2PxObr7teI/fT+kVkq0pbCE3wcNexkdsVLM2RjLf5YeYcGkrnRr5Hddr6G15p3Id/jq8FdMaTOF6e2nX3rnfd/B4sng2wjQUJANhdlQlGvZ7t/cUuw9/f/53OxUOPADpJ+CjvdCQOkd5DGrYdEkyE0DFDS7BZoMhJ1zIHEf1GoC4RMs12w8A67rPVYkKfjiiv7YO5d/7f0v/dxCeXrwYnq8tY6IdsG8PbJ69klfD517nu8/v5F3PBzwUSb+70w8LQqLwCsYpu8AFy+jI1a4/CIzvd5ZS52a7vx4/yW6WS4jtyiXeQfnMWv/LO5qfhdPdXrq0n8tnT8Jn94ItVvD+N/+3uo2F0Nh1l8t/WuVcQailkLj/uBbOm2E1nBkCWx413IBWJks6yY4e1puxCvKhd7PQhNjl/qUPnxxWQnZCTyzbwZtisy8PvgLvtxymkJzCVN6yRQC10K51+SOgTP4KiERZS5iXGgoywe/BFmJlpu0qgFXJxP392pE5KnzHIjPuKrnnM48zUtbXmL4L8PptqAbs/bPIqJRBE92evLSxd5cDIumWC6ujpj1z6JucrRcoL3erpcaIdBl8l/FHizHahEBUzfCA9ug+8OQlQTnTgAKcs/BoomQEX99x6wE0sIXvLR0HEtSd7G03h143fAMN7yxmu5htfh0bEejo9mnpIOcdfPmsS3PsydlD/e61efBI5twmrgaQjoYna7CZeQV0eX1VYzoEMrrw1tfcr9CcyFzD85lzv45ODo40jGwI61qtaKNfxu6BXXDdHGx1hpyUuH8KTj4o6W7bMRn0Ob2Cn5HV+lcLMzsAUHtYNwSw/r5ZT58cUnxpzfxS+ouRmoPgno+zZwtp8nML2aqtO6vX+1W1ALmDJjDWzve4vNj37MvJJi3f3uIwInrLK3PKqyGmxO3tA5myd4EnhvcHI8ypk4+mXGSB9c8yMnMk9xc/2ae6PQE/u4X9bObi2HbJ3BmF6Qdh3PH/+qbB2hzp+0Ue7BcHB78jmWUz+YZ0OMxoxP9Q9X+lycurzCX2SsfxMERJt48myJMzNt0gi4NfGlbx8fodHbP2eTMC91eoGNgR17a/AKjis5xz4/DadP1EVoGd8XDycPoiBVmdOc6/LQ7nt/2J3BHp7p/25aen8601dPIKsxiVr9ZZQ+pLDFbCueB76FmA6jVGOrfaCmqPnUtHwHNK+ndXIO2oy2jf9a+BsHtLVNw2BAp+NWV1sT9+gBLHIu4M7gXgbXb8vOeMyRk5PPqsFZGp6tSBjccTHPfZjy/bDwz8k/CukdwQHFXszE80fkyFyXtWMd6NWkc4MmCHXF/K/hF5iIeXfcoiTmJzBs4j3YB7f755JIS+PVhS7G/6QXo+XjlBS8vpWDIfyFhL3w1zNLn3+8lyy8qGyAXbaurkxuZmbgeRwdHJtz4ElprZm+IJSzAkz5NbW+omb1r4NOQb8ZsYFOfz/hUB3BLVjZfRX3DgtWPW7ouqhilFHd2rsveuHSikjIBKNEl/Gf7f4hMjuSV7q/8VeyL8uHUFji2Eo78Cr8+BHu+gp5P2Fex/x+3mnD/ZsuIneg/4KPOsOMzo1MBVmrhK6UGATMAEzBHa/3mRdtV6fbBQC4wXmu92xrHFtfn2Jb3WOrpwZgmt+Pv7s+m6LMcTszk7dva4FBFly+0BTXqduXGcau4Ieo3sre8yNvxK6g/azU3dH4IWt1WpeZ5uaGJA26By5m46hMcnXI4X3CeEl3ClDZTGFJ3AOz5Bo4ug+Nr/t43D3DDg9DnOWOCW4OzB/R+CjqOgyUPwrInLF1TjfsZGqvco3SUUibgGNAfiAd2AqO11ocv2Gcw8CCWgt8FmKG1vuKteDJKp2IUpURx188RJLt58fOoP6jpWpO7524nKimLTU/1wcXRdu8irEpyCrIY+8twknOTmZWQRPMSBxybDYEuU6BOZ6PjXbfYjFhm7JrBuvh1lGgNeY0Z0rwlwd7+1Peuzy01muHw00RI3AveodB0EIT1Aw9/MDlb7le4cDikvSvMgbkDIf00TFoDtcKu/JxyqOhROp2BGK11bOnBFgIRwOEL9okAvtSW3y7blFI+SqkgrXWiFY4vrtHc9U9zxMWZDzo/S03XmhyIz2Bj9FmeGNhUin0l8nDx4sObv2DM0jGMCQFHFPXSt9Jj0SrubzwK936vgLO70TGvyenM09y3/D6KSoq4t+W9hPvewsR5MRxXPrwysQtOB7+H73qDgyPc/hU0v9WuJyq7Ks4ecOc38FkfWDgaJq4y7C85a/ThhwBxFzyOL/3ete4DgFJqslIqUikVmZqaaoV44kJRCduZlRPDYCd/+ja1TOf73h9H8XF34p5uMklaZQv1CuX7W7/n1e6vck+rewmu14P5Pt6MSviNPXO6w4kNdrPASlJOEpNWTsKszXx181c80vERbmzQmDdGtCbyxFl2z5oCi6dA7TaWPu4WQ6t+sf+fmvXg9i8tY/V/fsCwc2qNFn5ZZ+zid3M1+1i+qfVsYDZYunTKF01cqMhcxPPrn8THXMIzN/4HgF2nzrPuaCpPDmqKl6uTwQmrp9oetf+2HN/OpJ28sP4JxuWd5Z5f72aaroFb6zug3Rib7epIyU1h0spJZBZmMmfgHBr6/DUqZXgrP5qun0OLlHUcb3QPjcb8t8rfi1Cm+jdC3xcts3Tu/Qbaj630CNZo4ccDdS54HAokXMc+ooKtPrmCo4XneM4xCJ+6lrHP7/9xlFqezoyv5ita2ZJOtTvx04iljAwbzvwa3gz3MbFlx//Bp90tw/0MVlRSREpuCkfSjrAgagETV0xkwI8DSMxJ5KO+H1lmtczPgJQjELMKvhxGi/R1zPeazJBjt5CcU/VGJV21btOh3o3w+1OWuYAqmTV+ze4EGiulGgBngDuBMRftswSYXtq/3wXIkP77yrfywBfUKjbT50bLULdtsWlsjknj+Vua4+5cDVtcNszDyYMXb3yVm8OG8srWV5hCMb0LNR0Xj6Z5/7doUb8PXs6VOxnbsfPHeG3ba+xO+fsAu/re9bmv1X0MaTCYhklR8NtAiNv21w4mZxj5Ob2DBvLSu+v4dvtpHu3fpFKz2wwHEwz/1PLLe/FUGL+0UqdgKPf/cq11sVJqOrACy7DMeVrrQ0qpqaXbZwLLsIzQicEyLPPe8h5XXJvcgkw2ph9lGO6YmgxCa837K48R6O3CWFngxGZ1qt2JH4f+yGf7P+OXYz+yLj8Ntj6Hyw5nRjWM4D73hvjnZ1uGdJY1BbAV5BfnM3v/bD4/+Dlezl5Maj2J2h618XX1paF3AxoW5lvuLv3qdsv0Bz51oc/z4NcQvEPALww8alEP6NXEnwU7TjP9pjCcTNX0NiCfupYpGBZPgaX/gm7TLHcSVwKZPK2aWL7mOZ6IW8K8FlPo1Gk6v+w9w8ML9/JKREvu6Vbf6HjiKp07uoyoXyayzNub31wdcdSaUVnZTMkuwKfNaMu87srBsmBHiRka9KRIlxCXHYeryRUfFx/cHN2ueHev1poDZw+w7MQylp9YTlp+GhGNIng8/HF8cIAT6y3dNdGrILN0dsiQcOj2ADSPuGQf/ZqoZO77IpKPxrRnSJtga/947IfWlruJd8+3PA5oYZlfv8O4cs+xL/PhV3fmIh6b14HdTorVd+8mOauIgR9soHGAJ99P6YZjdW1p2atDP8Ouz4kLasVnOo0lSVvxwIEH0s5xe0Y66SYHtru6ssvVhcNevkSbNEUlf/Wbu5hcaFijIc39mtOkZhMUiszCTDIKMkjOTSYpJ4kz2Wc4l38OZwdneno3Ygw16JSXaxlLnnLYskKUs5dlYZcmAy3j6L2vXMDNJZre764lqIYb30/pVoE/JDuRccZyd/HhX+D0FsvqWy2GQqdJULfrdY1ikoJfzeXu/IxeBz8gIqg7zw6YxV1ztrM/Pp1lD/egnl/VncCruog+H81bO99ie+J2vE2uZJrzAfBycKFFbjYtikpo3GIkRe41Sc9OJC03heiCNKIKznK+dF8At5ISAjER5F6b4FrNaaed6XtoBV7nT4GTR+mkZXUgsKWlwNfpAqZrH9k1a/1x3vg9iuWP9KBZbW+r/Rzs3tkYiJxruQPZ5AiPHQFHl2t+GSn41VlxIStmduRxL5g3YC77Ymrxn6VHeOu21v+YxVDYL601a+PWsvzkcpr7NqdLUBea1myKKf00LJoM8Tv++RzgrMkBB2cvvANb4xTYyrKE3+mtf+0U3B56PglNBoGDdf4SPJ9TSNc3VjOyYyivXWa+/GqrMAdSj1732gkyH351tucrVqoc/Jxq46ma8PbyrQxoEcjt4XWu/FxhN5RS3FT3Jm6qe9PfN/g2gHt/t1xUdXQBryDwDAQHE0qX4K9LwM3378U8MwGO/m5Z0LvRTVa/OaqmhzO3tg1m8Z4zPHVzM7zl/o+/c/aosIVypOBXZYW55K1/m421PLm1wc28sPgw7i4mXh/RukpOySsuweQIzQZf/f7ewdBpQsXlAcZ2rcePu+L5dV8Cd3WRUWKVRa7WVWU7ZrPIIZs8pXHMa0fkqfM8N7g5tTyvvV9QCGtqG1qDpoFe/BBpu+u/VkVS8KuqvHRit87gAz8/OgV05dsNTnRt6MvIjqFGJxMCpRSjwkPZG5fOseQso+NUG1Lwq6iizR/wdA1nXJ08cDw/hoIizWvDpStH2I7h7UNwdFD8EBl35Z2FVUjBr4qykvnkyFcccXHmrrCnWLk/l2l9wmjk72l0MiH+5OfpQt/mASzec4Yic4nRcaoFKfhV0N5l05nr5cZtdfpz7ER9vFwdmdLLNtbUFOJCt4fX4Wx2IWujUoyOUi1Iwa9i9OElvJ2+D39HD6Z1fonlh5IY0iYYVydZ2ETYnl5N/PH3cuF7uXhbKaTgVyW551i56gkOuLowvfMTbDyWSW6hmREdylxrRgjDOZocuK1DKGuPphB/PvfKTxDlIgW/Cin6/UlmuDsQ5lmHoWHDWbT7DHV83QivV9PoaEJc0pjOdXF1dODO2ds4cTbH6DhVmhT8qiJmFT+c/J04J0ce7fI0qVlFbD5+luHtQ2VkjrBpdf3cWTC5K7mFZkZ+uoWDZzKMjlRlScGvIrIj5zHTtyadA8PpEdKDn/eeQWsY0V66c4TtaxPqw49Tu+HqZOLO2ds4miRj8yuCFPyqoCiPr1K2cd5B8Vi4ZTWrn3bF07FeTerXktkwhX1o6O/JT/ffgLlEM3/rSaPjVElS8KuA/OgVLPB0pWfNFrSs1ZJDCZlEp2QzXFr3ws7UruHKza1r8+u+BPKLzEbHqXKk4FcBSw58wXmTifHhjwLwwapjeDibGNImyOBkQly7kR1DycovZuXhZKOjVDlS8O2cuSifL7OP0dLBg/CgLqw/lsqqIylMv6kxPu7ORscT4pp1beBHiI8bP+6SsfnWJgXfzq3bM4tTjibGNxhKcYnm1d8OU9/PnfturG90NCGui4OD4raOoWyKTiUpI//KTxBXTQq+nfsi+kdCis30C5/OV1tPEZOSzfO3tMDFUe6sFfbrtg4hlGhYtEda+dZUroKvlPJVSv2hlIou/VzmHT5KqXlKqRSl1MHyHE/83d6k3ewtTudu1zpkFLvw31XH6NG4Fn2bl2/VeyGMVs/Pg84NfPlxVzy2vAyrvSlvC/9pYLXWujGwuvRxWb4ABpXzWOIi3++bhZe5hOHNx/L6sihyC838+9YWcqOVqBJGdgwlNjWH3afTjY5SZZS34EcA80u/ng8MK2snrfUG4Fw5jyUuUGAuYE3yDvrm5bPbqSs/7Y5naq+GhAV4GR1NCKsY3DoId2cT3++U+fKtpbwFP1BrnQhQ+rncfQlKqclKqUilVGRqamp5X67K2hS7nBxdTH+/9jy1NI5G/h48eFNjo2MJYTWeLo4MbRvMkn0JZOUXGR2nSrhiwVdKrVJKHSzjI6IiAmmtZ2utw7XW4f7+/hVxiCph+b451DSb2adHk5CRx9sj28gUyKLKGd25LnlFZn7Zm2B0lCrB8Uo7aK37XWqbUipZKRWktU5USgUBsopBJcjNO8/67BMMwIf39rky/ob6dKzna3QsIayuTWgNWgR58+3209zVpa5cnyqn8nbpLAHGlX49DvilnK8nrsKGLW+SpxTZRf0I8HLhiYFNjY4kRIVQSjG6S10OJ2ZyQGbRLLfyFvw3gf5KqWigf+ljlFLBSqll/9tJKbUA2Ao0VUrFK6UmlPO41VeJmRUnfsdPK5acDOeOTnXwcLniH2pC2K2IdsG4OZlYsOO00VHsXrkqhdY6DehbxvcTgMEXPB5dnuOIv2Qf/IENphLCTW04qU2M6ljH6EhCVChvVydubRvEL3sTeO6WFnhKA+e6yZ229sRczNqt71DooDiQ2psbGvlR18/d6FRCVLjRneuSW2jmq62njI5i16Tg2xEdOY+FZFHL5E1CShB3dJLWvage2tXxoX+LQN5ZEcXKQ0lGx7FbUvDtRV46q7e+zX5XF2oxEm9XZwa2rG10KiEqhVKKGXe2o02oDw8u2MOuU+eNjmSXpODbiaL1bzHDw5H67sHsi2rMsPYhMu5eVCvuzo7MHRdOUA1XJszfyfHUbKMj2R0p+PYg7TiLD3/DSWcn2tW4j8Jixe3h0p0jqh8/Txfm39cZBbzws8zFeK2k4NuB3NUv84mPF+18W7J6dy3a1vGhVUgNo2MJYYh6fh5M6xPGluNpbI9NMzqOXZGCb+P0+VN8lLSBNJMDTVzvISE9nyflRitRzY3tWg9/L8uU4OLqScG3YRkFGTy8YiJf1fBiaOgAftrqSI/GtegeVsvoaEIYytXJxP29GrEt9hxbj0sr/2pJwbdRR9KOcMevt7MxP5GnnELxKpxIem4RT9/czOhoQtiEMV3qElDaypdFUq6OFHwbpLXmyQ1PUlSQyReJyQxq9zSfbz7JsHbBtAyWvnshwNLKn9YnjB0npJV/taTg26B9qfs4mXmS6Vn5tPVryVsHa6A1/GuA9N0LcaE7OtWhtrcr7648Kq38qyAF3wYtOb4ENwdnBiSf4GTYPfyw+wzju9enjq9MoyDEhVydTDzUtzG7T6ez+ojMzn4lUvBtTIG5gOUnl9PX7Ii7RwAPH6hPbW9XHuorq1kJUZZR4aE0qOXBOyuOYi6RVv7lSMG3MWvj1pJVmMXQpBNsrzuJfYl5PD+kucwQKMQlOJkceKx/E44mZ7Fk3xmj49g0Kfg2ZknUdwQWm2kX0InJh1vTPcyPW1oHGR1LCJt2S+sgWgR58/4fxygsLjE6js2Sgm9DzuamsiU5klvzCvnA9UHyikp4eWgrWdZNiCtwcFA8OagpcefyWLhTFkq5FCn4NmTpxpcxA13DxjP7gJnxN9QnLMDT6FhC2IVeTfzp3MCXD9fEkF9kNjqOTZKCbyOKcs7yY/waWmtnZib0w8vFkWl9woyOJYTdUErxWP8mpGYV8PU2WSilLFLwbcTCVY9y0tFE3zrjWXssjek3heHj7mx0LCHsSteGfnQP8+PTdcfJLSw2Oo7NkYJvA86mHeOTc7vp7uDN4sPtCPFx455u9Y2OJYRdeqx/E9JyCpm/RVr5FytXwVdK+Sql/lBKRZd+rlnGPnWUUmuVUkeUUoeUUg+X55hV0YzVj5CvFL1DHuPgmUwe699EFjcR4jp1rOdLryb+zNpwnKz8IqPj2JTytvCfBlZrrRsDq0sfX6wY+JfWujnQFZimlGpRzuNWGftOruHnvDjGOofy0c6aNKvtxbD2IUbHEsKuPda/Cem5RczbdNLoKDalvAU/Aphf+vV8YNjFO2itE7XWu0u/zgKOAFLRsEyS9uamF/AvNuPi/iDx5/N4aWhLTA4yDFOI8mhbx4dBLWszY/UxftoVb3Qcm1Hegh+otU4ES2EHAi63s1KqPtAe2H6ZfSYrpSKVUpGpqanljGfbNhxbzEFzJhPcmjNjp2JE+xC6NvQzOpYQVcL7d7SlWyM//vXDPr7ZLv35cBUFXym1Sil1sIyPiGs5kFLKE/gJeERrnXmp/bTWs7XW4VrrcH9//2s5hF3RWjMr8r8EFxWzNWMMbk4mnhnc3OhYQlQZlkXPO3FTswCeW3yQLzafMDqS4a5Y8LXW/bTWrcr4+AVIVkoFAZR+LnO6OqWUE5Zi/43WepE134C92hL7OweK07nNoSG/nXLliUHN8PdyMTqWEFWKq5OJmWM70q95AK8viyIxI8/oSIYqb5fOEmBc6dfjgF8u3kFZ5gWYCxzRWr9fzuNVCVprPt3xNrWLi1keP4K2oTUY07mu0bGEqJKcHR34960tKdGaWetjjY5jqPIW/DeB/kqpaKB/6WOUUsFKqWWl+3QH7gZuUkrtLf0YXM7j2rXtp9ewrzCN3tn+HC0O4d1RbeVCrRAVqI6vO8Pbh7Bgx2lSsvKNjmOYchV8rXWa1rqv1rpx6edzpd9P0FoPLv16k9Zaaa3baK3blX4su/wrV10luoRPt75OQHExm5NH8O6otjQO9DI6lhBV3rQ+YRSZS/hsQ/Vt5cudtpVIa807m19md0EKN53zpmePQdwsUx8LUSnq1/JgaNtgvt52mrTsAqPjGEIKfiWau/8zvj6+iDszcsj0fIQnBsoatUJUpuk3hZFfbGbupuo5YkcKfiVZHL2YGXs/5ObsHHT2XTx9z23Sby9EJQsL8GJw6yDmbjrB1uNpRsepdFLwK8HJjJO8vOUluuXl0T6lHXdMeJKaHjITphBGeGVoS+r6ujNh/k4iT54zOk6lkoJfCWbt+gDHEjN3J3sQfPsMuUgrhIH8PF34ZlIXanu7Mv7zneyNSzc6UqWRgl/BYtNjWRa3mjsyszkV/j69WtYxOpIQ1V6AlyvfTuqKr4cz4+btIDWrelzElYJfwWZufxOXkhJ8srowckBvo+MIIUrVruHKvPGdyC0s5o1lR4yOUymk4FegmPPRLE/cyoiMAhy7Pi1z3AthY8ICPJnSsxGL9pxhW2zVv4grBb8Cfbrp37jpEnIzBzLyxlZGxxFClGFanzBCa7rxws8HKTKXGB2nQknBryAbT6xk5bkD3JwBNTo/gJerk9GRhBBlcHM28fLQlkSnZDOvio/Pl4JfAaLP7OCJ9f+iaUEhsefGMP7GMKMjCSEuo2/zQPo1D2TG6mhOnM0xOk6FkYJvZWcTdzN95QTczWY8Em6jQccI/Dxl2mMhbN0rES1xdnTggW92k19kNjpOhZCCb0UFqUd5eOndpKFxPzOCZJ9BPNi3sdGxhBBXIdjHjfdvb8uRxExe+e2w0XEqhBR8aynK570lY9jv5IBL4mB8Q4fyw9Ru1JLWvRB246ZmgUzp1ZBvt5/ml71njI5jdVLwrWT1kgkscCwk8FwTejYby9xx4XKhVgg79PiApnSsV5NnFx1gY3TVWldbCr4VJER+xgsZewnMdyPA6zFeH94aJ5P8aIWwR04mBz4e04HQmu6Mm7eD2RuOo7U2OpZVSFUqp+KUKJ7a/R7FyoHk5Om8NaI9llUdhRD2qnYNVxY9cAODWtXm9WVRPLRwLwXF9n8hVwp+eZiL+PTXe9jr4kRx4q08NaAXdXzdjU4lhLACDxdHPh7TgScGNuXXfQn8949ooyOVm6PRAezZrpVPMseUS1BWfWr5D5WFyIWoYpRSTOsTRvz5PGZtOE7f5gF0qu9rdKzrJi3865R5YgPPJCzHp9iJtIwpvHVbGxxkQRMhqqTnbmlOaE03/vX9PnIKio2Oc92k4F8HXZDDv1dOI9lkwjVnCj/f31e6coSowjxdHHlvVDvizufymh3PrFmugq+U8lVK/aGUii79XLOMfVyVUjuUUvuUUoeUUi+X55hGy8pN55kv+rHKFVoUdOH7SROk2AtRDXRu4MvkHpYx+tO+3c2WmLN2N3qnvC38p4HVWuvGwOrSxxcrAG7SWrcF2gGDlFJdy3lcQ6w5vp0R3/ZhqWs2Xc1hzLt3JjXcZay9ENXFYwOaMKlHAzZFn2XMnO3c9N56DsRnGB3rqpW34EcA80u/ng8Mu3gHbZFd+tCp9MO+fi0Cb2/6nEc3TkSrfJ51vYnP7luMm7MUeyGqExdHE8/d0oLtz/blv3e0Jb/IzP3f7CIjr8joaFelvAU/UGudCFD6OaCsnZRSJqXUXiAF+ENrvf1SL6iUmqyUilRKRaam2sZdbv9d/gZfHX+fbnl5zA0ew+g7ZhgdSQhhIFcnE8Pbh/LxXR1IysjnmUX77aJ754oFXym1Sil1sIyPiKs9iNbarLVuB4QCnZVSl1wNRGs9W2sdrrUO9/f3v9pDVIy883w5fzifJ31DeF4xr7d/nno3v2BsJiGEzehQtyaPD2zKsgNJfLP9tNFxruiK4/C11v0utU0playUCtJaJyqlgrC04C/3WulKqXXAIODgtYatTLkp0Xz1/Qg+9dTUL/TizZE/4lsrxOhYQggbM7lHQ7YcT+OV3w4TFuBJ14Z+Rke6pPJ26SwBxpV+PQ745eIdlFL+Simf0q/dgH5AVDmPW2G01sz540NGLYngIy8ILGnAZ6OXEyjFXghRBgcHxfu3tyXQ24XRn23jhZ8PkpVvm3365S34bwL9lVLRQP/SxyilgpVSy0r3CQLWKqX2Azux9OH/Vs7jVoioxFOMmHszMxJmU4Jiesg0fh//C4FeNYyOJoSwYbU8XVj+cE/G31Cfr7efov/7G1hxKMnoWP+gbPlCQ3h4uI6MjKzw45TkZ/HlT8/wef5askyK8bmuTLhjER5+MlWCEOLa7I1L5+mf9hOVlMWglrV5OaIlgd6ulXZ8pdQurXV4mduqc8EvSTnKxuVvsCJzM796uRJS5MCLzR7ghu6TQWa8FEJcpyJzCbM3xDJjdTQuJgem9m7E6M518fVwrvBjS8G/QHFmAnu2zuHI8eVscEhlu5srTiWK7t438NbQ93F3krtmhRDWceJsDi8tOcT6Y6m4ODowtG0wo8Lr0KGuD44VtGZGtS745uIith9YxNrDiziUe4xox0LyHSw/aE+zMz1qj+CpPg/g5/aPWSGEEMIqjiVnMX/LSRbtPkNekRkvV0duDKtFp/q+hAV40ijAkyBvV6tMwFjtCn7EZ63JcdDkKk2ug8Jc2j1TvwCCCSE4sBe92wyhe93mOJpkhmghROXIyi9ic8xZ1h9LZd3RVBIz8v/cppRlkjZvVyeCfVz5YeoN13WMyxX8KlntArQXqtgBF+WME64EeoTRo+3ddGkRjkmmMBZCGMTL1YlBrYIY1CoIrTVpOYXEpGQTk5JNcmY+WfnFZOYX4VxR3T1VsYUvhBDV1eVa+DIfvhBCVBNS8IUQopqQgi+EENWEFHwhhKgmpOALIUQ1IQVfCCGqCSn4QghRTUjBF0KIasKmb7xSSqUCp67z6bWAs1aMU9nsPT/Y/3uw9/xg/+9B8l+7elrrMteHtemCXx5KqchL3W1mD+w9P9j/e7D3/GD/70HyW5d06QghRDUhBV8IIaqJqlzwZxsdoJzsPT/Y/3uw9/xg/+9B8ltRle3DF0II8XdVuYUvhBDiAlLwhRCimrDrgq+UGqSUOqqUilFKPV3GdqWU+r/S7fuVUh2MyHk5V/EeeiulMpRSe0s/XjQi56UopeYppVKUUgcvsd2mz8FV5Lf1n38dpdRapdQRpdQhpdTDZexj6+fgat6DzZ4HpZSrUmqHUmpfaf6Xy9jHNs6B1touPwATcBxoCDgD+4AWF+0zGPgdUEBXYLvRua/jPfQGfjM662XeQ0+gA3DwEttt/RxcKb+t//yDgA6lX3sBx+zw/8HVvAebPQ+lP1fP0q+dgO1AV1s8B/bcwu8MxGitY7XWhcBCIOKifSKAL7XFNsBHKRVU2UEv42reg03TWm8Azl1mF5s+B1eR36ZprRO11rtLv84CjgAhF+1m6+fgat6DzSr9uWaXPnQq/bh4NIxNnAN7LvghQNwFj+P55z+Sq9nHSFebr1vpn4u/K6VaVk40q7H1c3A17OLnr5SqD7TH0sK8kN2cg8u8B7Dh86CUMiml9gIpwB9aa5s8B46VfUArUmV87+Lfqlezj5GuJt9uLHNjZCulBgM/A40rOpgV2fo5uBK7+PkrpTyBn4BHtNaZF28u4yk2dw6u8B5s+jxorc1AO6WUD7BYKdVKa33hdSGbOAf23MKPB+pc8DgUSLiOfYx0xXxa68z//bmotV4GOCmlalVexHKz9XNwWfbw81dKOWEplN9orReVsYvNn4MrvQd7OA8AWut0YB0w6KJNNnEO7Lng7wQaK6UaKKWcgTuBJRftswS4p/QKeVcgQ2udWNlBL+OK70EpVVsppUq/7ozlnKVVetLrZ+vn4LJs/edfmm0ucERr/f4ldrPpc3A178GWz4NSyr+0ZY9Syg3oB0RdtJtNnAO77dLRWhcrpaYDK7CMdpmntT6klJpaun0msAzL1fEYIBe416i8ZbnK9zASuF8pVQzkAXfq0sv+tkAptQDLCIpaSql44N9YLlrZxTm4ivw2/fMHugN3AwdK+5ABngXqgn2cA67uPdjyeQgC5iulTFh+EX2vtf7NFmuRTK0ghBDVhD136QghhLgGUvCFEKKakIIvhBDVhBR8IYSoJqTgCyFENSEFXwghqgkp+EIIUU38P/AZiaMEMW6TAAAAAElFTkSuQmCC\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "#### Your code goes here\n", + "import numpy as np\n", + "import qiskit\n", + "import matplotlib.pyplot as plt\n", "\n", "#A helpful starting point here is to remember that the magnetization can be measured by examining each bitstring \n", "# from the results.\n", + "#### Your code goes here\n", + "import numpy as np\n", + "import qiskit\n", + "from qiskit import QuantumCircuit\n", + "import matplotlib.pyplot as plt\n", + "from qiskit import *\n", + "# from qiskit import Aer\n", "\n", + "#Note in the example plot, the parameters J = g = 1.0\n", "\n", - "\n" + "#Recall that the results are returned as a dict object with the bitstring as keys and the number of counts as values.\n", + "# A suggestion to run this quickly is to use the Aer simulator backend. For extra points, plot the time evolution\n", + "# using a real device\n", + "initial_state_vector = [\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 1,\n", + " 0,\n", + " 0\n", + "]\n", + "\n", + "# Define function for operating gates on the quantum circuit object\n", + "#\n", + "# params: qc - quantum circuit to gate\n", + "# params: t - time at which operation takes place\n", + "# params: J - zz coupling constant\n", + "# params: g - x interaction constant\n", + "# params: m - number of trotter steps\n", + "def U_trotter(initial_state, t, J, g, m):\n", + " m_steps = np.linspace(0,m,m)\n", + " theta_one = t * J / m\n", + " theta_two = theta_one * g\n", + " for i in m_steps:\n", + " initial_state.rzz(2*theta_one,0,1)\n", + " initial_state.rzz(2*theta_one,1,2)\n", + " initial_state.rx(2*theta_two,0)\n", + " initial_state.rx(2*theta_two,1)\n", + " initial_state.rx(2*theta_two,2)\n", + " return initial_state\n", + "\n", + "# Define function for operating gates on the quantum circuit object\n", + "#\n", + "# params: s - iterable to sum bits over\n", + "def bitsum(s):\n", + " bitsum = 0\n", + " for n in s:\n", + " bitsum += int(n)\n", + " return bitsum\n", + "\n", + "# array of time points and constants\n", + "ts = np.linspace(0, np.pi, 100)\n", + "J = 1.0\n", + "g = 1.\n", + "sim = Aer.get_backend('aer_simulator')\n", + "\n", + "shots = 2**14 # number of samples used for statistics\n", + "\n", + "# Loop for all ms\n", + "m_list = [1,5,10]\n", + "for m in m_list:\n", + " mag_list = []\n", + " # Loop for all times\n", + " for t in ts:\n", + " initial_state = QuantumCircuit(3,3)\n", + " initial_state.initialize(initial_state_vector, [0,1,2])\n", + " \n", + " # Run the circuit and measure\n", + " qc = U_trotter(initial_state, t, J, g, m)\n", + " qc.measure_all(add_bits = False)\n", + "\n", + " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", + " qc_trans = qiskit.compiler.transpile(qc, sim)\n", + " counts = sim.run(qc_trans, shots=shots).result().get_counts()\n", + "\n", + " # calculate the probabilities for each computational basis\n", + " probs = {}\n", + " # initialize mag term and add it to the list\n", + " prob_mag = {}\n", + " mag_term = 0.\n", + " for output in ['000','001', '010', '011', '100', '101', '110', '111']:\n", + " # if the state is there, calculate the portion of the sum and add it to the current mag value\n", + " if output in counts:\n", + " probs[output] = counts[output]/shots\n", + " # otherwise leave the value unchanged\n", + " else:\n", + " probs[output] = 0\n", + " mag_term += probs[output] * (3. - (2. * bitsum(output)))\n", + "\n", + " mag_list.append(mag_term/3.)\n", + "\n", + " plt.plot(ts, mag_list)\n", + "plt.show()\n" ] }, { @@ -453,8 +726,97 @@ "outputs": [], "source": [ "#### Your code goes here\n", + "import numpy as np\n", + "import qiskit\n", + "import matplotlib.pyplot as plt\n", "\n", - "\n" + "import numpy as np\n", + "import qiskit\n", + "from qiskit import QuantumCircuit\n", + "import matplotlib.pyplot as plt\n", + "from qiskit import *\n", + "\n", + "initial_state_vector = [\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 1,\n", + " 0,\n", + " 0\n", + "]\n", + "\n", + "# Define function for operating gates on the quantum circuit object\n", + "#\n", + "# params: qc - quantum circuit to gate\n", + "# params: t - time at which operation takes place\n", + "# params: J - zz coupling constant\n", + "# params: g - x interaction constant\n", + "# params: m - number of trotter steps\n", + "def U_trotter(initial_state, t, J, g, m):\n", + " m_steps = np.linspace(0,m,m)\n", + " theta_one = t * J / m\n", + " theta_two = theta_one * g\n", + " for i in m_steps:\n", + " initial_state.rzz(2*theta_one,0,1)\n", + " initial_state.rzz(2*theta_one,1,2)\n", + " initial_state.rx(2*theta_two,0)\n", + " initial_state.rx(2*theta_two,1)\n", + " initial_state.rx(2*theta_two,2)\n", + " return initial_state\n", + "\n", + "# Define function for operating gates on the quantum circuit object\n", + "#\n", + "# params: s - iterable to sum bits over\n", + "def bitsum(s):\n", + " bitsum = 0\n", + " for n in s:\n", + " bitsum += int(n)\n", + " return bitsum\n", + "\n", + "# array of time points and constants\n", + "ts = np.linspace(0, np.pi, 100)\n", + "J = 1.0\n", + "g = 1.\n", + "sim = Aer.get_backend('aer_simulator')\n", + "\n", + "shots = 2**14 # number of samples used for statistics\n", + "\n", + "# Loop for all ms\n", + "m = 10\n", + "mag_list = []\n", + "prob_list = []\n", + "# Loop for all times\n", + "for t in ts:\n", + " initial_state = QuantumCircuit(3,3)\n", + " initial_state.initialize(initial_state_vector, [0,1,2])\n", + "\n", + " # Run the circuit and measure\n", + " qc = U_trotter(initial_state, t, J, g, m)\n", + " qc.measure_all(add_bits = False)\n", + "\n", + " # run the circuit with the selected measurement and get the number of samples that output each bit value\n", + " qc_trans = qiskit.compiler.transpile(qc, sim)\n", + " counts = sim.run(qc_trans, shots=shots).result().get_counts()\n", + "\n", + " # calculate the probabilities for each computational basis\n", + " probs = {}\n", + " # initialize mag term and add it to the list\n", + " prob_mag = {}\n", + " mag_term = 0.\n", + " for output in ['000','001', '010', '011', '100', '101', '110', '111']:\n", + " # if the state is there, calculate the portion of the sum and add it to the current mag value\n", + " if output in counts:\n", + " probs[output] = counts[output]/shots\n", + " # otherwise leave the value unchanged\n", + " else:\n", + " probs[output] = 0\n", + " mag_term += probs[output] * (3. - (2. * bitsum(output)))\n", + "\n", + " mag_list.append(mag_term/3.)\n", + "\n", + "plt.plot(ts, mag_list)\n" ] } ], @@ -474,7 +836,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" + "version": "3.9.7" }, "toc": { "base_numbering": 1, diff --git a/Lab-3 Quantum Phase Estimation/Lab03_QPE.ipynb b/Lab-3 Quantum Phase Estimation/Lab03_QPE.ipynb index 58419c9..405f3f8 100644 --- a/Lab-3 Quantum Phase Estimation/Lab03_QPE.ipynb +++ b/Lab-3 Quantum Phase Estimation/Lab03_QPE.ipynb @@ -23,9 +23,18 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\Tyler\\AppData\\Local\\Temp/ipykernel_6420/35548535.py:6: DeprecationWarning: The qiskit.ignis package is deprecated and has been supersceded by the qiskit-experiments project. Refer to the migration guide: https://github.com/Qiskit/qiskit-ignis#migration-guide on how to migrate to the new project.\n", + " from qiskit.ignis.mitigation.measurement import *\n" + ] + } + ], "source": [ "from qiskit import *\n", "import numpy as np\n", @@ -82,7 +91,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -122,30 +131,178 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "
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4/═════════════════════════════════════════════════════════════════════════»\n", + "« »\n", + "« ┌─┐ \n", + "«q_0: ───────────────┤M├────────────────────────\n", + "« └╥┘ ┌─┐ \n", + "«q_1: ──────■─────────╫───────────┤M├───────────\n", + "« ┌───┐ │ ║ └╥┘ ┌─┐ \n", + "«q_2: ┤ H ├─┼─────────╫──■─────────╫──────┤M├───\n", + "« └───┘ │P(-π/4) ║ │P(-π/2) ║ ┌───┐└╥┘┌─┐\n", + "«q_3: ──────■─────────╫──■─────────╫─┤ H ├─╫─┤M├\n", + "« ║ ║ └───┘ ║ └╥┘\n", + "«q_4: ────────────────╫────────────╫───────╫──╫─\n", + "« ║ ║ ║ ║ \n", + "«c: 4/════════════════╩════════════╩═══════╩══╩═\n", + "« 0 1 2 3 " + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "## Start your code to create the circuit, qc4\n", - "\n", - "\n", - "\n", + "from qiskit import *\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", "\n", + "## Start your code to create the circuit, qc4\n", "\n", + "# Create and set up circuit\n", + "qc4 = QuantumCircuit(5, 4)\n", "\n", + "# Apply H-Gates to counting qubits:\n", + "for qubit in range(4):\n", + " qc4.h(qubit)\n", "\n", + "# Prepare our eigenstate |psi>:\n", + "qc4.x(4)\n", "\n", + "# Do the controlled-U operations:\n", + "angle = 2*math.pi/3\n", + "repetitions = 1\n", + "for counting_qubit in range(4):\n", + " for i in range(repetitions):\n", + " qc4.cp(angle, counting_qubit, 4);\n", + " repetitions *= 2\n", "\n", + "# Do the inverse QFT:\n", + "qft_dagger(qc4, 4)\n", "\n", + "# Measure of course!\n", + "for n in range(4):\n", + " qc4.measure(n,n)\n", "\n", - "qc4.draw()" + "qc4.draw()\n" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "## Run this cell to simulate 'qc4' and to plot the histogram of the result\n", "sim = Aer.get_backend('aer_simulator')\n", @@ -188,8 +345,22 @@ "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ + "t = 4\n", + "\n", "phi_est = np.array([round(int(key, 2)/2**t,3) for key in list(count_qc4.keys())])\n", "key_new = list(map(str, phi_est))\n", "count_new = dict(zip(key_new, count_qc4.values()))\n", @@ -220,20 +391,56 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 40, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3\n" + ] + } + ], "source": [ - "## Your code goes here\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "# from qiskit import *\n", + "import numpy as np\n", + "# from qiskit.visualization import plot_histogram\n", + "# import qiskit.tools.jupyter\n", + "# from qiskit.tools.monitor import job_monitor\n", + "# from qiskit.ignis.mitigation.measurement import *\n", + "import matplotlib.pyplot as plt\n", "\n", + "## Your code goes here\n", "\n", - "\n" + "b = 0.3125\n", + "start = 0\n", + "m_list = []\n", + "sum = 0.\n", + "for i in range(16):\n", + " m_list.append(sum)\n", + " if m_list[i] == b:\n", + " start = i\n", + " sum += 1/16\n", + "\n", + "# constants\n", + "phi = 1/3. #actual phase\n", + "e = -1 #starting e (start at -1 because loop increments at the beginning)\n", + "diff = np.abs(phi - m_list[start]) #difference between phi and the bit estimation value\n", + "accuracy = 2.**(-2) #desired accuracy\n", + "lower_bound = start #lower bound for loop\n", + "upper_bound = start #upper bound for loop\n", + "\n", + "# Loop, while the difference is less than or equal to the accuracy, increment e and check the largest difference between phi and the 2 next bit estimations\n", + "while diff <= accuracy:\n", + " e += 1\n", + " lower_bound -= 1\n", + " upper_bound += 1\n", + " lower_diff = np.abs(phi - m_list[lower_bound])\n", + " upper_diff = np.abs(phi - m_list[upper_bound])\n", + " diff = max(lower_diff,upper_diff)\n", + "\n", + "print(e)\n" ] }, { @@ -252,23 +459,112 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 43, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "here!\n", + "0\n", + "0001\n" + ] + } + ], "source": [ - "## Your code goes here\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "# from qiskit import *\n", + "import numpy as np\n", + "# from qiskit.visualization import plot_histogram\n", + "# import qiskit.tools.jupyter\n", + "# from qiskit.tools.monitor import job_monitor\n", + "# from qiskit.ignis.mitigation.measurement import *\n", + "import matplotlib.pyplot as plt\n", "\n", + "## Your code goes here\n", "\n", + "# probability of success = sum of probabilities of the bits that are allowed (within e)\n", + "# Note that e will be all bits that are +- e bits\n", + "# so we need to start at the start bit, which we already have!\n", + "# then we need to calculate e, which we already have!\n", + "# then, we can sum those probabilities!\n", + "\n", + "b = 0.3125\n", + "start = 0\n", + "m_list = []\n", + "sum = 0.\n", + "for i in range(16):\n", + " m_list.append(sum)\n", + " if m_list[i] == b:\n", + " start = i\n", + " sum += 1/16\n", + "\n", + "# constants\n", + "phi = 1/3. #actual phase\n", + "e = -1 #starting e (start at -1 because loop increments at the beginning)\n", + "diff = np.abs(phi - m_list[start]) #difference between phi and the bit estimation value\n", + "accuracy = 2.**(-2) #desired accuracy\n", + "lower_bound = start #lower bound for loop\n", + "upper_bound = start #upper bound for loop\n", + "\n", + "# Loop, while the difference is less than or equal to the accuracy, increment e and check the largest difference between phi and the 2 next bit estimations\n", + "while diff <= accuracy:\n", + " e += 1\n", + " lower_bound -= 1\n", + " upper_bound -= 1\n", + " lower_diff = np.abs(phi - m_list[lower_bound])\n", + " upper_diff = np.abs(phi - m_list[upper_bound])\n", + " diff = max(lower_diff,upper_diff)\n", + "\n", + "# now we have e, so we need to add the probabilities!\n", + "# so we need to loop through the dict and take the count values at the proper places and calculate probabilities!\n", + "# Loop to find the most significant bit string\n", + "bit_count = 0\n", + "for option in count_qc4:\n", + " bit_count_comparison = count_qc4[option]\n", + " bit_count = max(bit_count, bit_count_comparison)\n", + " if bit_count == bit_count_comparison:\n", + " most_sig_bit_string = option\n", + "\n", + "# Now need to loop through bits e away from the bit we found, and calculate probabilities!\n", + "# make a list of bits allowed\n", + "list_allowed_start = start - e\n", + "list_index = list_allowed_start\n", + "list_allowed_end = start + e\n", + "bit_list = []\n", + "while list_index <= list_allowed_end:\n", + " bit_list.append(list_index)\n", + " list_index +=1\n", + " \n", + "# Now make a list of the keys that will work\n", + "# for bit in bit_list:\n", + " \n", + "# print(bit/2)\n", + "# if \n", + " \n", + "# try to convert to a bit string\n", + "val = 2\n", + "val_char_string = '0000'\n", + "new_val = val / 2\n", + "while new_val > 0:\n", + " new_val = int(new_val/2)\n", + " if math.remainder(new_val,2) == 0:\n", + " val_char_string = val_char_string.replace('0','',1)\n", + " val_char_string = val_char_string + '1'\n", + " print(\"here!\")\n", + " else:\n", + " val_char_string = val_char_string.replace('0','',1)\n", + " val_char_string = val_char_string + '0'\n", + " print(new_val)\n", + "print(val_char_string)\n", + " \n", "\n", - "\n" + "# dict_index = 0\n", + "# print(count_qc4)\n", + "# for option in count_qc4:\n", + "# if dict_index in bit_list:\n", + "# print(option)\n", + "# dict_index += 1" ] }, { @@ -294,1648 +590,20 @@ }, { "cell_type": "code", - 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Eigensolver/.ipynb_checkpoints/Lab-4_Calculating-Molecular-Ground-States-checkpoint.ipynb b/Lab-4 Variational Quantum Eigensolver/.ipynb_checkpoints/Lab-4_Calculating-Molecular-Ground-States-checkpoint.ipynb index e582b04..0ac084d 100644 --- a/Lab-4 Variational Quantum Eigensolver/.ipynb_checkpoints/Lab-4_Calculating-Molecular-Ground-States-checkpoint.ipynb +++ b/Lab-4 Variational Quantum Eigensolver/.ipynb_checkpoints/Lab-4_Calculating-Molecular-Ground-States-checkpoint.ipynb @@ -35,7 +35,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 1, "id": "9ffdfafe", "metadata": { "scrolled": true @@ -49,10 +49,10 @@ "\n", "ElectronicEnergy : Fermionic Operator\n", "register length=4, number terms=14\n", - " (0.18093120148374148+0j) * ( +_0 -_1 +_2 -_3 )\n", - "+ (-0.18093120148374137+0j) * ( +_0 -_1 -_2 +_3 )\n", - "+ (-0.18093120148374137+0j) * ( -_0 +_1 +_2 -_3 )\n", - "+ (0.1809312014837414+0j) * ( -_0 +_1 -_2 +_3 ) ... \n", + " (0.18093120148374142+0j) * ( +_0 -_1 +_2 -_3 )\n", + "+ (-0.18093120148374134+0j) * ( +_0 -_1 -_2 +_3 )\n", + "+ (-0.18093120148374134+0j) * ( -_0 +_1 +_2 -_3 )\n", + "+ (0.18093120148374128+0j) * ( -_0 +_1 -_2 +_3 ... \n", "\n", "ParticleNumber : Fermionic Operator\n", "register length=4, number terms=4\n", @@ -125,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 2, "id": "b1bdd324", "metadata": {}, "outputs": [ @@ -133,21 +133,21 @@ "name": "stdout", "output_type": "stream", "text": [ - "-0.810547996598181 * IIII\n", - "- 0.22575350027942787 * ZIII\n", - "+ 0.17218394351950983 * IZII\n", - "+ 0.12091263344524696 * ZZII\n", - "- 0.22575350027942784 * IIZI\n", - "+ 0.1746434349614699 * ZIZI\n", - "+ 0.1661454338161823 * IZZI\n", + "-0.8105479965981814 * IIII\n", + "- 0.22575350027942775 * ZIII\n", + "+ 0.17218394351950977 * IZII\n", + "+ 0.12091263344524698 * ZZII\n", + "- 0.22575350027942775 * IIZI\n", + "+ 0.17464343496146983 * ZIZI\n", + "+ 0.16614543381618233 * IZZI\n", "+ 0.1721839435195099 * IIIZ\n", - "+ 0.1661454338161823 * ZIIZ\n", - "+ 0.16892754063368898 * IZIZ\n", - "+ 0.12091263344524696 * IIZZ\n", - "+ 0.045232800370935355 * XXXX\n", - "+ 0.045232800370935355 * YYXX\n", - "+ 0.045232800370935355 * XXYY\n", - "+ 0.045232800370935355 * YYYY\n" + "+ 0.16614543381618233 * ZIIZ\n", + "+ 0.1689275406336891 * IZIZ\n", + "+ 0.12091263344524698 * IIZZ\n", + "+ 0.045232800370935335 * XXXX\n", + "+ 0.045232800370935335 * YYXX\n", + "+ 0.045232800370935335 * XXYY\n", + "+ 0.045232800370935335 * YYYY\n" ] } ], @@ -171,7 +171,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 3, "id": "cb446832", "metadata": {}, "outputs": [ @@ -179,11 +179,11 @@ "name": "stdout", "output_type": "stream", "text": [ - "(-1.0523732634886747-2.7755575615628914e-17j) * II\n", - "+ (-0.3979374437989376+1.3877787807814457e-17j) * ZI\n", - "+ 0.3979374437989376 * IZ\n", - "+ (-0.011280107962794245+1.3877787807814457e-17j) * ZZ\n", - "+ (0.1809312014837414+3.469446951953614e-18j) * XX\n" + "(-1.052373263488675-2.7755575615628914e-17j) * II\n", + "- 0.39793744379893736 * ZI\n", + "+ (0.3979374437989376-2.7755575615628914e-17j) * IZ\n", + "+ (-0.011280107962794272+2.7755575615628914e-17j) * ZZ\n", + "+ (0.18093120148374128-3.469446951953614e-18j) * XX\n" ] } ], @@ -222,7 +222,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 4, "id": "8abb9437", "metadata": {}, "outputs": [], @@ -259,14 +259,12 @@ "spsa = SPSA(maxiter=iterations)\n", "vqe = VQE(ansatz, optimizer=spsa, callback=store_intermediate_result, quantum_instance=qi)\n", "\n", - "\n", - "\n", "result = vqe.compute_minimum_eigenvalue(operator=H2_op)" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 5, "id": "13e09aea", "metadata": {}, "outputs": [ @@ -276,13 +274,13 @@ "Text(0.5, 1.0, 'Convergence with no noise')" ] }, - "execution_count": 12, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -313,7 +311,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 6, "id": "b05105ad", "metadata": {}, "outputs": [ @@ -350,11 +348,86 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "id": "745cf220", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Convergence with no noise')" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ + "from qiskit.utils import QuantumInstance, algorithm_globals\n", + "from qiskit import Aer\n", + "from qiskit.algorithms.optimizers import COBYLA\n", + "from qiskit.algorithms.optimizers import SLSQP\n", + "from qiskit.algorithms.optimizers import L_BFGS_B\n", + "from qiskit.algorithms import VQE, NumPyMinimumEigensolver\n", + "from qiskit.circuit.library import EfficientSU2\n", + "import matplotlib.pyplot as plt\n", + "\n", + "seed = 170\n", + "iterations = 125\n", + "algorithm_globals.random_seed = seed\n", + "backend = Aer.get_backend('statevector_simulator')\n", + "qi = QuantumInstance(backend=backend, seed_simulator=seed, seed_transpiler=seed)\n", + "\n", + "#List of optimizers, values and counts\n", + "opt_list = []\n", + "opt_list.append(COBYLA(maxiter=iterations))\n", + "opt_list.append(SLSQP(maxiter=iterations))\n", + "opt_list.append(L_BFGS_B(maxiter=iterations))\n", + "counts_list = []\n", + "values_list = []\n", + "result_list = []\n", + "\n", + "def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + "\n", + "#Run through each optimizer and make lists of values\n", + "for i in range(0,3):\n", + " counts = []\n", + " values = []\n", + "\n", + " ansatz = EfficientSU2(num_qubits=4, entanglement='linear')\n", + " opt = opt_list[i]\n", + " vqe = VQE(ansatz, optimizer=opt, callback=store_intermediate_result, quantum_instance=qi)\n", + "\n", + " counts_list.append(counts)\n", + " values_list.append(values)\n", + "\n", + " result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n", + " result_list.append(result)\n", + " \n", + "fig = plt.figure(figsize=(12, 4))\n", + "ax = fig.add_axes([1,1,1,1])\n", + "ax.plot(counts_list[0], values_list[0])\n", + "ax.plot(counts_list[1], values_list[1])\n", + "ax.plot(counts_list[2], values_list[2])\n", + "ax.set_xlabel('Eval count', size=18)\n", + "ax.set_ylabel('Energy', size=18)\n", + "ax.set_title('Convergence with no noise', size=20)\n", + "\n", "#You'll need to import the COBYLA, SLSQP, and L_BFGS_B optimizers the same way for SPSA above. When \n", "# initialized as a variable, you can set (among other things) the max number of iterations. The default is 1000\n", "# and you may want to use a smaller amount when testing out your code.\n", @@ -375,17 +448,97 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 30, "id": "2e01cb12", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VQE on stat vector qasm simulator (no noise): -1.85727\n", + "Delta from reference energy value is 0.00000\n", + "VQE on stat vector qasm simulator (no noise): -1.85727\n", + "Delta from reference energy value is 0.00000\n", + "VQE on stat vector qasm simulator (no noise): -1.85728\n", + "Delta from reference energy value is 0.00000\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "#Modify the data you've gathered above using the reference value calculated with the NumpyMinimumEigenSolver()\n", "#\n", "#\n", "# Your code goes here\n", "#\n", - "#" + "#\n", + "\n", + "#Calculate the real solution\n", + "npme = NumPyMinimumEigensolver()\n", + "result_npme = npme.compute_minimum_eigenvalue(operator=H2_op)\n", + "ref_value = result_npme.eigenvalue.real\n", + "\n", + "#List of optimizers, values and counts\n", + "opt_list = []\n", + "opt_list.append(COBYLA(maxiter=iterations))\n", + "opt_list.append(SLSQP(maxiter=iterations))\n", + "opt_list.append(L_BFGS_B(maxiter=iterations))\n", + "counts_list = []\n", + "values_list = []\n", + "result_list = []\n", + "#also need a list of the difference values!\n", + "ref_en_diff_list = []\n", + "\n", + "def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + " #append the reference energy difference\n", + " ref_en_diff.append(mean - ref_value)\n", + "\n", + "#Run through each optimizer and make lists of values\n", + "for i in range(0,3):\n", + " counts = []\n", + " values = []\n", + " ref_en_diff = []\n", + "\n", + " ansatz = EfficientSU2(num_qubits=4, entanglement='linear')\n", + " opt = opt_list[i]\n", + " vqe = VQE(ansatz, optimizer=opt, callback=store_intermediate_result, quantum_instance=qi)\n", + "\n", + " counts_list.append(counts)\n", + " values_list.append(values)\n", + " ref_en_diff_list.append(ref_en_diff)\n", + "\n", + " result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n", + " result_list.append(result)\n", + " \n", + "fig = plt.figure(figsize=(12, 4))\n", + "ax = fig.add_axes([1,1,1,1])\n", + "ax.plot(counts_list[0], ref_en_diff_list[0])\n", + "ax.plot(counts_list[1], ref_en_diff_list[1])\n", + "ax.plot(counts_list[2], ref_en_diff_list[2])\n", + "ax.set_xlabel('Eval count', size=18)\n", + "ax.set_ylabel('Energy', size=18)\n", + "ax.set_title('Convergence with no noise', size=20)\n", + "\n", + "#Go through and calc differences in energy for each simulator\n", + "for i in range(0,3):\n", + " print(f'VQE on stat vector qasm simulator (no noise): {result_list[i].eigenvalue.real:.5f}')\n", + " print(f'Delta from reference energy value is {(result_list[i].eigenvalue.real - ref_value):.5f}')\n", + "\n", + "#Now need to run through the VQE for each optimizer, take the difference at each step, and plot that!" ] }, { @@ -409,7 +562,49 @@ "#\n", "# Your code goes here\n", "#\n", - "#" + "#\n", + "from qiskit_nature.drivers import UnitsType, Molecule\n", + "from qiskit_nature.drivers.second_quantization import (\n", + " ElectronicStructureDriverType,\n", + " ElectronicStructureMoleculeDriver,\n", + ")\n", + "from qiskit_nature.problems.second_quantization import ElectronicStructureProblem\n", + "import qiskit_nature as qk_nature\n", + "qk_nature.settings.dict_aux_operators = True\n", + "\n", + "\n", + "#Initalize the driver for the H2 molecule. The input for this are the element symbol as string followed by\n", + "# an array of x, y, z positions in units of angstroms.\n", + "# We need to do this for multiple positions, see if we can make multiple objects?\n", + "# I want a range of what values? let's go from 50% of our current position to 150% of it.\n", + "# how many steps? lets do 50 different steps, so we make 50 different objects!\n", + "\n", + "# list of molecules\n", + "molecule_list = []\n", + "\n", + "# list of diffs\n", + "equil_spacing = 0.735 #equilibrium spacing\n", + "min_dist = equil_spacing * 0.5 #closest spacing\n", + "max_dist = equil_spacing * 1.5 #farthest spacing\n", + "num_spacings = 10\n", + "dist_list = np.linspace(min_dist,max_dist,num_spacings)\n", + "\n", + "for i in dist_list:\n", + " molecule = Molecule(\n", + " geometry=[[\"H\", [0.0, 0.0, 0.0]], [\"H\", [0.0, 0.0, 0.735]]])\n", + "\n", + "\n", + " driver = ElectronicStructureMoleculeDriver(\n", + " molecule, basis=\"sto3g\", driver_type=ElectronicStructureDriverType.PYQUANTE)\n", + "\n", + "\n", + " #This prepares the second quantized fermionic operator after computing the one and two body orbitals\n", + " es_problem = ElectronicStructureProblem(driver)\n", + " second_q_op = es_problem.second_q_ops()\n", + "\n", + " print(\"Items of the second_q_op dict: \\n\")\n", + " for key, val in second_q_op.items():\n", + " print(key,':', val, '\\n')" ] }, { @@ -424,20 +619,153 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "83c75b76", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.0 * XXI\n", + "- 1.0 * IXX\n", + "- 1.0 * YYI\n", + "- 1.0 * IYY\n", + "- 1.0 * ZII\n", + "- 1.0 * IZI\n", + "- 1.0 * IIZ\n", + "-3.828427124746195\n", + "VQE on stat vector qasm simulator (no noise): -3.73792\n", + "Delta from reference energy value is 0.09051\n", + "VQE on stat vector qasm simulator (no noise): -3.82843\n", + "Delta from reference energy value is 0.00000\n", + "VQE on stat vector qasm simulator (no noise): -3.82843\n", + "Delta from reference energy value is 0.00000\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ + "from qiskit.utils import QuantumInstance, algorithm_globals\n", + "from qiskit import Aer\n", + "from qiskit.algorithms.optimizers import COBYLA\n", + "from qiskit.algorithms.optimizers import SLSQP\n", + "from qiskit.algorithms.optimizers import L_BFGS_B\n", + "from qiskit.algorithms import VQE, NumPyMinimumEigensolver\n", + "from qiskit.circuit.library import EfficientSU2\n", + "import matplotlib.pyplot as plt\n", + "\n", "#Compare the VQE result with the exact eigenvalue using the NumpyMinimumEigenSolver(). I'd recommend keeping\n", "# the total size of the operators to be < 5 qubits. You should just need the Pauli ops imported below.\n", "#\n", "from qiskit.opflow import I, X, Y, Z\n", "#\n", "# Your code goes here\n", - "#\n", - "#" + "\n", + "#Hamiltonian for Ising model\n", + "def H_XX(J: float, g: float):\n", + " #Interactions (I is the identity matrix; X and Z are Pauli matrices; ^ is a tensor product; * multiplies a scalar)\n", + " XXs = (X^X^I) + (I^X^X) + (Y^Y^I) + (I^Y^Y)\n", + " Zs = (Z^I^I) + (I^Z^I) + (I^I^Z)\n", + " H = -J*(XXs) - (g*Zs)\n", + " return H\n", + "\n", + "J = 1\n", + "g = 1\n", + "H = H_XX(J,g)\n", + "print(H)\n", + "\n", + "#Calculate the real solution\n", + "npme = NumPyMinimumEigensolver()\n", + "result_npme = npme.compute_minimum_eigenvalue(operator=H)\n", + "ref_value = result_npme.eigenvalue.real\n", + "print(ref_value)\n", + "\n", + "#Constants for ansantz calculations\n", + "ansatz = EfficientSU2(num_qubits=3, entanglement='linear')\n", + "seed = 170\n", + "iterations = 125\n", + "algorithm_globals.random_seed = seed\n", + "backend = Aer.get_backend('statevector_simulator')\n", + "qi = QuantumInstance(backend=backend, seed_simulator=seed, seed_transpiler=seed)\n", + "\n", + "#List of optimizers, values and counts\n", + "opt_list = []\n", + "opt_list.append(COBYLA(maxiter=iterations))\n", + "opt_list.append(SLSQP(maxiter=iterations))\n", + "opt_list.append(L_BFGS_B(maxiter=iterations))\n", + "counts_list = []\n", + "values_list = []\n", + "result_list = []\n", + "#also need a list of the difference values!\n", + "ref_en_diff_list = []\n", + "\n", + "def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + " #append the reference energy difference\n", + " ref_en_diff.append(mean - ref_value)\n", + "\n", + "#Run through each optimizer and make lists of values\n", + "for i in range(0,3):\n", + " counts = []\n", + " values = []\n", + " ref_en_diff = []\n", + "\n", + " ansatz = EfficientSU2(num_qubits=4, entanglement='linear')\n", + " opt = opt_list[i]\n", + " vqe = VQE(ansatz, optimizer=opt, callback=store_intermediate_result, quantum_instance=qi)\n", + "\n", + " counts_list.append(counts)\n", + " values_list.append(values)\n", + " ref_en_diff_list.append(ref_en_diff)\n", + "\n", + " result = vqe.compute_minimum_eigenvalue(operator=H)\n", + " result_list.append(result)\n", + " \n", + "fig = plt.figure(figsize=(12, 4))\n", + "ax = fig.add_axes([1,1,1,1])\n", + "ax.plot(counts_list[0], ref_en_diff_list[0])\n", + "ax.plot(counts_list[1], ref_en_diff_list[1])\n", + "ax.plot(counts_list[2], ref_en_diff_list[2])\n", + "ax.set_xlabel('Eval count', size=18)\n", + "ax.set_ylabel('Energy', size=18)\n", + "ax.set_title('Convergence with no noise', size=20)\n", + "\n", + "#Go through and calc differences in energy for each simulator\n", + "for i in range(0,3):\n", + " print(f'VQE on stat vector qasm simulator (no noise): {result_list[i].eigenvalue.real:.5f}')\n", + " print(f'Delta from reference energy value is {(result_list[i].eigenvalue.real - ref_value):.5f}')\n", + "\n", + "#Now need to run through the VQE for each optimizer, take the difference at each step, and plot that!" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1f4b1e9b", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c508933f", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -456,7 +784,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" + "version": "3.9.7" }, "toc": { "base_numbering": 1, diff --git a/Lab-4 Variational Quantum Eigensolver/Lab-4_Calculating-Molecular-Ground-States.ipynb b/Lab-4 Variational Quantum Eigensolver/Lab-4_Calculating-Molecular-Ground-States.ipynb index e582b04..0ac084d 100644 --- a/Lab-4 Variational Quantum Eigensolver/Lab-4_Calculating-Molecular-Ground-States.ipynb +++ b/Lab-4 Variational Quantum Eigensolver/Lab-4_Calculating-Molecular-Ground-States.ipynb @@ -35,7 +35,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 1, "id": "9ffdfafe", "metadata": { "scrolled": true @@ -49,10 +49,10 @@ "\n", "ElectronicEnergy : Fermionic Operator\n", "register length=4, number terms=14\n", - " (0.18093120148374148+0j) * ( +_0 -_1 +_2 -_3 )\n", - "+ (-0.18093120148374137+0j) * ( +_0 -_1 -_2 +_3 )\n", - "+ (-0.18093120148374137+0j) * ( -_0 +_1 +_2 -_3 )\n", - "+ (0.1809312014837414+0j) * ( -_0 +_1 -_2 +_3 ) ... \n", + " (0.18093120148374142+0j) * ( +_0 -_1 +_2 -_3 )\n", + "+ (-0.18093120148374134+0j) * ( +_0 -_1 -_2 +_3 )\n", + "+ (-0.18093120148374134+0j) * ( -_0 +_1 +_2 -_3 )\n", + "+ (0.18093120148374128+0j) * ( -_0 +_1 -_2 +_3 ... \n", "\n", "ParticleNumber : Fermionic Operator\n", "register length=4, number terms=4\n", @@ -125,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 2, "id": "b1bdd324", "metadata": {}, "outputs": [ @@ -133,21 +133,21 @@ "name": "stdout", "output_type": "stream", "text": [ - "-0.810547996598181 * IIII\n", - "- 0.22575350027942787 * ZIII\n", - "+ 0.17218394351950983 * IZII\n", - "+ 0.12091263344524696 * ZZII\n", - "- 0.22575350027942784 * IIZI\n", - "+ 0.1746434349614699 * ZIZI\n", - "+ 0.1661454338161823 * IZZI\n", + "-0.8105479965981814 * IIII\n", + "- 0.22575350027942775 * ZIII\n", + "+ 0.17218394351950977 * IZII\n", + "+ 0.12091263344524698 * ZZII\n", + "- 0.22575350027942775 * IIZI\n", + "+ 0.17464343496146983 * ZIZI\n", + "+ 0.16614543381618233 * IZZI\n", "+ 0.1721839435195099 * IIIZ\n", - "+ 0.1661454338161823 * ZIIZ\n", - "+ 0.16892754063368898 * IZIZ\n", - "+ 0.12091263344524696 * IIZZ\n", - "+ 0.045232800370935355 * XXXX\n", - "+ 0.045232800370935355 * YYXX\n", - "+ 0.045232800370935355 * XXYY\n", - "+ 0.045232800370935355 * YYYY\n" + "+ 0.16614543381618233 * ZIIZ\n", + "+ 0.1689275406336891 * IZIZ\n", + "+ 0.12091263344524698 * IIZZ\n", + "+ 0.045232800370935335 * XXXX\n", + "+ 0.045232800370935335 * YYXX\n", + "+ 0.045232800370935335 * XXYY\n", + "+ 0.045232800370935335 * YYYY\n" ] } ], @@ -171,7 +171,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 3, "id": "cb446832", "metadata": {}, "outputs": [ @@ -179,11 +179,11 @@ "name": "stdout", "output_type": "stream", "text": [ - "(-1.0523732634886747-2.7755575615628914e-17j) * II\n", - "+ (-0.3979374437989376+1.3877787807814457e-17j) * ZI\n", - "+ 0.3979374437989376 * IZ\n", - "+ (-0.011280107962794245+1.3877787807814457e-17j) * ZZ\n", - "+ (0.1809312014837414+3.469446951953614e-18j) * XX\n" + "(-1.052373263488675-2.7755575615628914e-17j) * II\n", + "- 0.39793744379893736 * ZI\n", + "+ (0.3979374437989376-2.7755575615628914e-17j) * IZ\n", + "+ (-0.011280107962794272+2.7755575615628914e-17j) * ZZ\n", + "+ (0.18093120148374128-3.469446951953614e-18j) * XX\n" ] } ], @@ -222,7 +222,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 4, "id": "8abb9437", "metadata": {}, "outputs": [], @@ -259,14 +259,12 @@ "spsa = SPSA(maxiter=iterations)\n", "vqe = VQE(ansatz, optimizer=spsa, callback=store_intermediate_result, quantum_instance=qi)\n", "\n", - "\n", - "\n", "result = vqe.compute_minimum_eigenvalue(operator=H2_op)" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 5, "id": "13e09aea", "metadata": {}, "outputs": [ @@ -276,13 +274,13 @@ "Text(0.5, 1.0, 'Convergence with no noise')" ] }, - "execution_count": 12, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -313,7 +311,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 6, "id": "b05105ad", "metadata": {}, "outputs": [ @@ -350,11 +348,86 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "id": "745cf220", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Convergence with no noise')" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ + "from qiskit.utils import QuantumInstance, algorithm_globals\n", + "from qiskit import Aer\n", + "from qiskit.algorithms.optimizers import COBYLA\n", + "from qiskit.algorithms.optimizers import SLSQP\n", + "from qiskit.algorithms.optimizers import L_BFGS_B\n", + "from qiskit.algorithms import VQE, NumPyMinimumEigensolver\n", + "from qiskit.circuit.library import EfficientSU2\n", + "import matplotlib.pyplot as plt\n", + "\n", + "seed = 170\n", + "iterations = 125\n", + "algorithm_globals.random_seed = seed\n", + "backend = Aer.get_backend('statevector_simulator')\n", + "qi = QuantumInstance(backend=backend, seed_simulator=seed, seed_transpiler=seed)\n", + "\n", + "#List of optimizers, values and counts\n", + "opt_list = []\n", + "opt_list.append(COBYLA(maxiter=iterations))\n", + "opt_list.append(SLSQP(maxiter=iterations))\n", + "opt_list.append(L_BFGS_B(maxiter=iterations))\n", + "counts_list = []\n", + "values_list = []\n", + "result_list = []\n", + "\n", + "def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + "\n", + "#Run through each optimizer and make lists of values\n", + "for i in range(0,3):\n", + " counts = []\n", + " values = []\n", + "\n", + " ansatz = EfficientSU2(num_qubits=4, entanglement='linear')\n", + " opt = opt_list[i]\n", + " vqe = VQE(ansatz, optimizer=opt, callback=store_intermediate_result, quantum_instance=qi)\n", + "\n", + " counts_list.append(counts)\n", + " values_list.append(values)\n", + "\n", + " result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n", + " result_list.append(result)\n", + " \n", + "fig = plt.figure(figsize=(12, 4))\n", + "ax = fig.add_axes([1,1,1,1])\n", + "ax.plot(counts_list[0], values_list[0])\n", + "ax.plot(counts_list[1], values_list[1])\n", + "ax.plot(counts_list[2], values_list[2])\n", + "ax.set_xlabel('Eval count', size=18)\n", + "ax.set_ylabel('Energy', size=18)\n", + "ax.set_title('Convergence with no noise', size=20)\n", + "\n", "#You'll need to import the COBYLA, SLSQP, and L_BFGS_B optimizers the same way for SPSA above. When \n", "# initialized as a variable, you can set (among other things) the max number of iterations. The default is 1000\n", "# and you may want to use a smaller amount when testing out your code.\n", @@ -375,17 +448,97 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 30, "id": "2e01cb12", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VQE on stat vector qasm simulator (no noise): -1.85727\n", + "Delta from reference energy value is 0.00000\n", + "VQE on stat vector qasm simulator (no noise): -1.85727\n", + "Delta from reference energy value is 0.00000\n", + "VQE on stat vector qasm simulator (no noise): -1.85728\n", + "Delta from reference energy value is 0.00000\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "#Modify the data you've gathered above using the reference value calculated with the NumpyMinimumEigenSolver()\n", "#\n", "#\n", "# Your code goes here\n", "#\n", - "#" + "#\n", + "\n", + "#Calculate the real solution\n", + "npme = NumPyMinimumEigensolver()\n", + "result_npme = npme.compute_minimum_eigenvalue(operator=H2_op)\n", + "ref_value = result_npme.eigenvalue.real\n", + "\n", + "#List of optimizers, values and counts\n", + "opt_list = []\n", + "opt_list.append(COBYLA(maxiter=iterations))\n", + "opt_list.append(SLSQP(maxiter=iterations))\n", + "opt_list.append(L_BFGS_B(maxiter=iterations))\n", + "counts_list = []\n", + "values_list = []\n", + "result_list = []\n", + "#also need a list of the difference values!\n", + "ref_en_diff_list = []\n", + "\n", + "def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + " #append the reference energy difference\n", + " ref_en_diff.append(mean - ref_value)\n", + "\n", + "#Run through each optimizer and make lists of values\n", + "for i in range(0,3):\n", + " counts = []\n", + " values = []\n", + " ref_en_diff = []\n", + "\n", + " ansatz = EfficientSU2(num_qubits=4, entanglement='linear')\n", + " opt = opt_list[i]\n", + " vqe = VQE(ansatz, optimizer=opt, callback=store_intermediate_result, quantum_instance=qi)\n", + "\n", + " counts_list.append(counts)\n", + " values_list.append(values)\n", + " ref_en_diff_list.append(ref_en_diff)\n", + "\n", + " result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n", + " result_list.append(result)\n", + " \n", + "fig = plt.figure(figsize=(12, 4))\n", + "ax = fig.add_axes([1,1,1,1])\n", + "ax.plot(counts_list[0], ref_en_diff_list[0])\n", + "ax.plot(counts_list[1], ref_en_diff_list[1])\n", + "ax.plot(counts_list[2], ref_en_diff_list[2])\n", + "ax.set_xlabel('Eval count', size=18)\n", + "ax.set_ylabel('Energy', size=18)\n", + "ax.set_title('Convergence with no noise', size=20)\n", + "\n", + "#Go through and calc differences in energy for each simulator\n", + "for i in range(0,3):\n", + " print(f'VQE on stat vector qasm simulator (no noise): {result_list[i].eigenvalue.real:.5f}')\n", + " print(f'Delta from reference energy value is {(result_list[i].eigenvalue.real - ref_value):.5f}')\n", + "\n", + "#Now need to run through the VQE for each optimizer, take the difference at each step, and plot that!" ] }, { @@ -409,7 +562,49 @@ "#\n", "# Your code goes here\n", "#\n", - "#" + "#\n", + "from qiskit_nature.drivers import UnitsType, Molecule\n", + "from qiskit_nature.drivers.second_quantization import (\n", + " ElectronicStructureDriverType,\n", + " ElectronicStructureMoleculeDriver,\n", + ")\n", + "from qiskit_nature.problems.second_quantization import ElectronicStructureProblem\n", + "import qiskit_nature as qk_nature\n", + "qk_nature.settings.dict_aux_operators = True\n", + "\n", + "\n", + "#Initalize the driver for the H2 molecule. The input for this are the element symbol as string followed by\n", + "# an array of x, y, z positions in units of angstroms.\n", + "# We need to do this for multiple positions, see if we can make multiple objects?\n", + "# I want a range of what values? let's go from 50% of our current position to 150% of it.\n", + "# how many steps? lets do 50 different steps, so we make 50 different objects!\n", + "\n", + "# list of molecules\n", + "molecule_list = []\n", + "\n", + "# list of diffs\n", + "equil_spacing = 0.735 #equilibrium spacing\n", + "min_dist = equil_spacing * 0.5 #closest spacing\n", + "max_dist = equil_spacing * 1.5 #farthest spacing\n", + "num_spacings = 10\n", + "dist_list = np.linspace(min_dist,max_dist,num_spacings)\n", + "\n", + "for i in dist_list:\n", + " molecule = Molecule(\n", + " geometry=[[\"H\", [0.0, 0.0, 0.0]], [\"H\", [0.0, 0.0, 0.735]]])\n", + "\n", + "\n", + " driver = ElectronicStructureMoleculeDriver(\n", + " molecule, basis=\"sto3g\", driver_type=ElectronicStructureDriverType.PYQUANTE)\n", + "\n", + "\n", + " #This prepares the second quantized fermionic operator after computing the one and two body orbitals\n", + " es_problem = ElectronicStructureProblem(driver)\n", + " second_q_op = es_problem.second_q_ops()\n", + "\n", + " print(\"Items of the second_q_op dict: \\n\")\n", + " for key, val in second_q_op.items():\n", + " print(key,':', val, '\\n')" ] }, { @@ -424,20 +619,153 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "83c75b76", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.0 * XXI\n", + "- 1.0 * IXX\n", + "- 1.0 * YYI\n", + "- 1.0 * IYY\n", + "- 1.0 * ZII\n", + "- 1.0 * IZI\n", + "- 1.0 * IIZ\n", + "-3.828427124746195\n", + "VQE on stat vector qasm simulator (no noise): -3.73792\n", + "Delta from reference energy value is 0.09051\n", + "VQE on stat vector qasm simulator (no noise): -3.82843\n", + "Delta from reference energy value is 0.00000\n", + "VQE on stat vector qasm simulator (no noise): -3.82843\n", + "Delta from reference energy value is 0.00000\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ + "from qiskit.utils import QuantumInstance, algorithm_globals\n", + "from qiskit import Aer\n", + "from qiskit.algorithms.optimizers import COBYLA\n", + "from qiskit.algorithms.optimizers import SLSQP\n", + "from qiskit.algorithms.optimizers import L_BFGS_B\n", + "from qiskit.algorithms import VQE, NumPyMinimumEigensolver\n", + "from qiskit.circuit.library import EfficientSU2\n", + "import matplotlib.pyplot as plt\n", + "\n", "#Compare the VQE result with the exact eigenvalue using the NumpyMinimumEigenSolver(). I'd recommend keeping\n", "# the total size of the operators to be < 5 qubits. You should just need the Pauli ops imported below.\n", "#\n", "from qiskit.opflow import I, X, Y, Z\n", "#\n", "# Your code goes here\n", - "#\n", - "#" + "\n", + "#Hamiltonian for Ising model\n", + "def H_XX(J: float, g: float):\n", + " #Interactions (I is the identity matrix; X and Z are Pauli matrices; ^ is a tensor product; * multiplies a scalar)\n", + " XXs = (X^X^I) + (I^X^X) + (Y^Y^I) + (I^Y^Y)\n", + " Zs = (Z^I^I) + (I^Z^I) + (I^I^Z)\n", + " H = -J*(XXs) - (g*Zs)\n", + " return H\n", + "\n", + "J = 1\n", + "g = 1\n", + "H = H_XX(J,g)\n", + "print(H)\n", + "\n", + "#Calculate the real solution\n", + "npme = NumPyMinimumEigensolver()\n", + "result_npme = npme.compute_minimum_eigenvalue(operator=H)\n", + "ref_value = result_npme.eigenvalue.real\n", + "print(ref_value)\n", + "\n", + "#Constants for ansantz calculations\n", + "ansatz = EfficientSU2(num_qubits=3, entanglement='linear')\n", + "seed = 170\n", + "iterations = 125\n", + "algorithm_globals.random_seed = seed\n", + "backend = Aer.get_backend('statevector_simulator')\n", + "qi = QuantumInstance(backend=backend, seed_simulator=seed, seed_transpiler=seed)\n", + "\n", + "#List of optimizers, values and counts\n", + "opt_list = []\n", + "opt_list.append(COBYLA(maxiter=iterations))\n", + "opt_list.append(SLSQP(maxiter=iterations))\n", + "opt_list.append(L_BFGS_B(maxiter=iterations))\n", + "counts_list = []\n", + "values_list = []\n", + "result_list = []\n", + "#also need a list of the difference values!\n", + "ref_en_diff_list = []\n", + "\n", + "def store_intermediate_result(eval_count, parameters, mean, std):\n", + " counts.append(eval_count)\n", + " values.append(mean)\n", + " #append the reference energy difference\n", + " ref_en_diff.append(mean - ref_value)\n", + "\n", + "#Run through each optimizer and make lists of values\n", + "for i in range(0,3):\n", + " counts = []\n", + " values = []\n", + " ref_en_diff = []\n", + "\n", + " ansatz = EfficientSU2(num_qubits=4, entanglement='linear')\n", + " opt = opt_list[i]\n", + " vqe = VQE(ansatz, optimizer=opt, callback=store_intermediate_result, quantum_instance=qi)\n", + "\n", + " counts_list.append(counts)\n", + " values_list.append(values)\n", + " ref_en_diff_list.append(ref_en_diff)\n", + "\n", + " result = vqe.compute_minimum_eigenvalue(operator=H)\n", + " result_list.append(result)\n", + " \n", + "fig = plt.figure(figsize=(12, 4))\n", + "ax = fig.add_axes([1,1,1,1])\n", + "ax.plot(counts_list[0], ref_en_diff_list[0])\n", + "ax.plot(counts_list[1], ref_en_diff_list[1])\n", + "ax.plot(counts_list[2], ref_en_diff_list[2])\n", + "ax.set_xlabel('Eval count', size=18)\n", + "ax.set_ylabel('Energy', size=18)\n", + "ax.set_title('Convergence with no noise', size=20)\n", + "\n", + "#Go through and calc differences in energy for each simulator\n", + "for i in range(0,3):\n", + " print(f'VQE on stat vector qasm simulator (no noise): {result_list[i].eigenvalue.real:.5f}')\n", + " print(f'Delta from reference energy value is {(result_list[i].eigenvalue.real - ref_value):.5f}')\n", + "\n", + "#Now need to run through the VQE for each optimizer, take the difference at each step, and plot that!" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1f4b1e9b", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c508933f", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -456,7 +784,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" + "version": "3.9.7" }, "toc": { "base_numbering": 1, diff --git a/Lab-4 Variational Quantum Eigensolver/Lab-4_Intro-VariationalQuantumEigensolver.ipynb b/Lab-4 Variational Quantum Eigensolver/Lab-4_Intro-VariationalQuantumEigensolver.ipynb index 8adcf3f..c6acca4 100644 --- a/Lab-4 Variational Quantum Eigensolver/Lab-4_Intro-VariationalQuantumEigensolver.ipynb +++ b/Lab-4 Variational Quantum Eigensolver/Lab-4_Intro-VariationalQuantumEigensolver.ipynb @@ -394,7 +394,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" + "version": "3.9.7" }, "toc": { "base_numbering": 1,