QV experiment (qiskit-community#32)

Co-authored-by: Gadi Aleksandrowicz <gadia@il.ibm.com>

qiskit_experiments/__init__.py

@@ -59,3 +59,4 @@
 from . import analysis
 from . import randomized_benchmarking
 from . import tomography
+from . import quantum_volume

qiskit_experiments/quantum_volume/__init__.py

@@ -0,0 +1,15 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021.
+#
+# 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.
+
+"""Quantum Volume Experiment Classes."""
+from .qv_experiment import QuantumVolume
+from .qv_analysis import QuantumVolumeAnalysis

qiskit_experiments/quantum_volume/qv_analysis.py

@@ -0,0 +1,266 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021.
+#
+# 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.
+"""
+Quantum Volume analysis class.
+"""
+
+import math
+import warnings
+from typing import Optional
+import numpy as np
+
+from qiskit_experiments.base_analysis import BaseAnalysis
+from qiskit_experiments.base_analysis import AnalysisResult
+from qiskit_experiments.analysis import plotting
+
+
+class QuantumVolumeAnalysis(BaseAnalysis):
+    """Quantum Volume Analysis class."""
+
+    # pylint: disable = arguments-differ
+    def _run_analysis(
+        self,
+        experiment_data,
+        plot: bool = True,
+        ax: Optional["plotting.pyplot.AxesSubplot"] = None,
+    ):
+        """Run analysis on circuit data.
+        Args:
+            experiment_data (ExperimentData): the experiment data to analyze.
+            plot: If True generate a plot of fitted data.
+            ax: Optional, matplotlib axis to add plot to.
+        Returns:
+            tuple: A pair ``(analysis_result, figures)`` where
+                   ``analysis_results`` may be a single or list of
+                   AnalysisResult objects, and ``figures`` may be
+                   None, a single figure, or a list of figures.
+        """
+        depth = experiment_data.experiment.num_qubits
+        data = experiment_data.data()
+        num_trials = len(data)
+        heavy_output_prob_exp = []
+
+        for data_trial in data:
+            heavy_output = self._calc_ideal_heavy_output(
+                data_trial["metadata"]["ideal_probabilities"], data_trial["metadata"]["depth"]
+            )
+            heavy_output_prob_exp.append(
+                self._calc_exp_heavy_output_probability(data_trial, heavy_output)
+            )
+
+        analysis_result = AnalysisResult(
+            self._calc_quantum_volume(heavy_output_prob_exp, depth, num_trials)
+        )
+
+        if plot and plotting.HAS_MATPLOTLIB:
+            ax = self._format_plot(ax, analysis_result)
+            figures = [ax.get_figure()]
+        else:
+            figures = None
+        return [analysis_result], figures
+
+    @staticmethod
+    def _calc_ideal_heavy_output(probabilities_vector, depth):
+        """
+        Calculate the bit strings of the heavy output for the ideal simulation
+        Args:
+            ideal_data (dict): the simulation result of the ideal circuit
+        Returns:
+             list: the bit strings of the heavy output
+        """
+
+        format_spec = "{0:0%db}" % depth
+        # Keys are bit strings and values are probabilities of observing those strings
+        all_output_prob_ideal = {
+            format_spec.format(b): float(np.real(probabilities_vector[b]))
+            for b in range(2 ** depth)
+        }
+
+        median_probabilities = float(np.real(np.median(probabilities_vector)))
+        heavy_strings = list(
+            filter(
+                lambda x: all_output_prob_ideal[x] > median_probabilities,
+                list(all_output_prob_ideal.keys()),
+            )
+        )
+        return heavy_strings
+
+    @staticmethod
+    def _calc_exp_heavy_output_probability(data, heavy_outputs):
+        """
+        Calculate the probability of measuring heavy output string in the data
+        Args:
+            data (dict): the result of the circuit exectution
+            heavy_outputs (list): the bit strings of the heavy output from the ideal simulation
+        Returns:
+            int: heavy output probability
+        """
+        circ_shots = sum(data["counts"].values())
+
+        # Calculate the number of heavy output counts in the experiment
+        heavy_output_counts = sum([data["counts"].get(value, 0) for value in heavy_outputs])
+
+        # Calculate the experimental heavy output probability
+        return heavy_output_counts / circ_shots
+
+    @staticmethod
+    def _calc_z_value(mean, sigma):
+        """Calculate z value using mean and sigma.
+
+        Args:
+            mean (float): mean
+            sigma (float): standard deviation
+
+        Returns:
+            float: z_value in standard normal distibution.
+        """
+
+        if sigma == 0:
+            # Assign a small value for sigma if sigma = 0
+            sigma = 1e-10
+            warnings.warn("Standard deviation sigma should not be zero.")
+
+        z_value = (mean - 2 / 3) / sigma
+
+        return z_value
+
+    @staticmethod
+    def _calc_confidence_level(z_value):
+        """Calculate confidence level using z value.
+
+        Accumulative probability for standard normal distribution
+        in [-z, +infinity] is 1/2 (1 + erf(z/sqrt(2))),
+        where z = (X - mu)/sigma = (hmean - 2/3)/sigma
+
+        Args:
+            z_value (float): z value in in standard normal distibution.
+
+        Returns:
+            float: confidence level in decimal (not percentage).
+        """
+
+        confidence_level = 0.5 * (1 + math.erf(z_value / 2 ** 0.5))
+
+        return confidence_level
+
+    def _calc_quantum_volume(self, heavy_output_prob_exp, depth, trials):
+        """
+        Calc the quantum volume of the analysed system.
+        quantum volume is determined by the largest successful depth.
+        A depth is successful if it has 'mean heavy-output probability' > 2/3 with confidence
+        level > 0.977 (corresponding to z_value = 2), and at least 100 trials have been ran.
+        we assume the error (standard deviation) of the heavy output probability is due to a
+        binomial distribution. standard deviation for binomial distribution is sqrt(np(1-p)),
+        where n is the number of trials and p is the success probability.
+
+        Returns:
+            dict: quantum volume calculations -
+            the quantum volume,
+            whether the results passed the threshold,
+            the confidence of the result,
+            the heavy output probability for each trial,
+            the mean heavy output probability,
+            the error of the heavy output probability,
+            the depth of the circuit,
+            the number of trials ran
+        """
+        quantum_volume = 1
+        success = False
+
+        mean_hop = np.mean(heavy_output_prob_exp)
+        sigma_hop = (mean_hop * ((1.0 - mean_hop) / trials)) ** 0.5
+        z = 2
+        threshold = 2 / 3 + z * sigma_hop
+        z_value = self._calc_z_value(mean_hop, sigma_hop)
+        confidence_level = self._calc_confidence_level(z_value)
+        # Must have at least 100 trials
+        if trials < 100:
+            warnings.warn("Must use at least 100 trials to consider Quantum Volume as successful.")
+        if mean_hop > threshold and trials >= 100:
+            quantum_volume = 2 ** depth
+            success = True
+
+        result = {
+            "quantum volume": quantum_volume,
+            "qv success": success,
+            "confidence": confidence_level,
+            "heavy output probability": heavy_output_prob_exp,
+            "mean hop": mean_hop,
+            "sigma": sigma_hop,
+            "depth": depth,
+            "trials": trials,
+        }
+        return result
+
+    @staticmethod
+    def _format_plot(ax, analysis_result):
+        """
+        Format the QV plot
+        Args:
+            ax: matplotlib axis to add plot to.
+            analysis_result: the results of the experimnt
+        Returns:
+            AxesSubPlot: the matplotlib axes containing the plot.
+        """
+        trial_list = np.arange(1, analysis_result["trials"] + 1)  # x data
+
+        hop_accumulative = np.cumsum(analysis_result["heavy output probability"]) / trial_list
+        two_sigma = 2 * (hop_accumulative * (1 - hop_accumulative) / trial_list) ** 0.5
+
+        # Plot inidivual HOP as scatter
+        ax = plotting.plot_scatter(
+            trial_list,
+            analysis_result["heavy output probability"],
+            ax=ax,
+            s=3,
+            zorder=3,
+            label="Individual HOP",
+        )
+        # Plot accumulative HOP
+        ax.plot(trial_list, hop_accumulative, color="r", label="Cumulative HOP")
+        # Plot two-sigma shaded area
+        ax = plotting.plot_errorbar(
+            trial_list,
+            hop_accumulative,
+            two_sigma,
+            ax=ax,
+            fmt="none",
+            ecolor="lightgray",
+            elinewidth=20,
+            capsize=0,
+            alpha=0.5,
+            label="2$\\sigma$",
+        )
+        # Plot 2/3 success threshold
+        ax.axhline(2 / 3, color="k", linestyle="dashed", linewidth=1, label="Threshold")
+
+        ax.set_ylim(
+            max(hop_accumulative[-1] - 4 * two_sigma[-1], 0),
+            min(hop_accumulative[-1] + 4 * two_sigma[-1], 1),
+        )
+
+        ax.set_xlabel("Number of Trials", fontsize=14)
+        ax.set_ylabel("Heavy Output Probability", fontsize=14)
+
+        ax.set_title(
+            "Quantum Volume experiment for depth "
+            + str(analysis_result["depth"])
+            + " - accumulative hop",
+            fontsize=14,
+        )
+
+        # Re-arrange legend order
+        handles, labels = ax.get_legend_handles_labels()
+        handles = [handles[1], handles[2], handles[0], handles[3]]
+        labels = [labels[1], labels[2], labels[0], labels[3]]
+        ax.legend(handles, labels)
+        return ax