Quantum Siren

Project aimed to investigate in the similarity between [1] and the inherent periodicity of parameterized gates within Variational Quantum Circuits. The general idea is to build a network that learns an implicit representation of a function. This function, generally speaking, maps some input to an output and therefore can be almost anything from a speech signal to an image. In case of the latter, the input would be the coordinate of a pixel and the output the pixel value itself.

Approach 📝

The current ansatz is the (un-)famous ‘Circuit 19’ approach from [2]. Data is encoded across all Qubits (i.e. Qubit 0 ← X coordinate, Qubit 1 ← Y coordinate, Qubit 2 ← X coordinate, …) using RY gates and Data-Reuploading. Initially I tried without data-reuploading but this resulted in a continuous color gradient across the whole image (barely any training effect):

• The main motivation for data-reuploading is, that, according to the paper, the number of encoding circuits determines the frequency in the function that the VQC can approximate
• Therefore my understanding is, that adding more layers should also increase the ‘sharpness’ of our image this correlates directly to the maximum (and number of) frequencies

Getting Started 🚀

This project is built using the Kedro Framework.

Install Dependencies 💾

Using pip:

pip install -r src/requirements.in

or

pip install -r src/requirements-gpu.in

if you want to have the GPU package of PyTorch

Using poetry:

poetry install

or

poetry install --extras='gpu'

if you want to have the GPU package of PyTorch

Running Experiments 🏃

Without further configuration you can execute

kedro run

which will load MNIST, preprocess the data and start training the model.

If want an overview of the nodes and pipelines, you can execute

kedro viz

which will open Kedro`s dashboard in you browser.

Configuration 🔧

The following parameters can be adjusted:

• Data Preprocessing Parameters: conf/base/parameters/preprocessing.yml
  • Batch size:
    • a number >0 indicating the batch size
    • -1 to use all of the data as batch
  • Mode: Type of dataset
    • "cosine": Fourier series
    • "image": Cameraman image
  • Domain: Range for the input data that goes into the encoding gates
  • Scale Domain by Pi: If the range shall be multiplied by Pi
  • Specific for 'Image' Dataset
    • Sidelength: Image sidelength
    • Nonlinear Coordinates: If an arcsin shall be applied on the coordinates
  • Specific for 'Cosine' Dataset
    • Omega: Frequencies for the Fourier series. List of lists where the "outer" list determines the dimensionality and the "inner" list the frequencies for that dimension
• Training Parameters: conf/base/parameters/data_science.yml
  • Number of qubits
  • Number of layers
  • Type of VQC ansatz. Currently available are:
    • "circuit_19"
    • "circuit_18"
  • Type of IEC ansatz. Currently available are:
    • "default": RX and RY for both image axis as subsequent gates acting on each qubit
    • "spread_layers": RX and RY alternating across the available qubits
  • Data reuploading as float value [0..1]
    • 1 means each layer has data reuploading
    • 0.5 means each second layer has data reuploading
    • 0 means no data reuploading is applied
  • Number of training steps
  • Shots (none/ number of shots)
  • Learning rate
  • Optimizer. Currently, only "Adam" is available
  • Loss. Currently available are:
    • "mse": Mean Square Error
    • "ssim": Structural Similarity Index Measure
    • "fft_ssim": Same as SSIM but measured in the frequency domain
    • "psnr": Peak Signal-to-Noise Ratio
  • Output interpretation. Currently available are:
    • "all": Measurement of all qubits and normalization
    • Index of a specific qubit

Literature 📚

[1]: Implicit Neural Representations with Periodic Activation Functions
[2]: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
[3]: The effect of data encoding on the expressive power of variational quantum machine learning models