# This code is part of Qiskit.
#
# (C) Copyright IBM 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.
"""Multi state discrimination analysis."""
from typing import List, Tuple, TYPE_CHECKING
import matplotlib
import numpy as np
from qiskit.providers.options import Options
from qiskit_experiments.framework import BaseAnalysis, AnalysisResultData, ExperimentData
from qiskit_experiments.data_processing import SkQDA
from qiskit_experiments.visualization import BasePlotter, IQPlotter, MplDrawer, PlotStyle
from qiskit_experiments.warnings import HAS_SKLEARN
if TYPE_CHECKING:
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
[docs]
class MultiStateDiscriminationAnalysis(BaseAnalysis):
r"""This class fits a multi-state discriminator to the data.
The class will report the configuration of the discriminator in the analysis result as well as
the fidelity of the discrimination reported as
.. math::
F = 1 - \frac{1}{d}\sum{i\neq j}P(i|j)
Here, :math:`d` is the number of levels that were discriminated while :math:`P(i|j)` is the
probability of measuring outcome :math:`i` given that state :math:`j` was prepared.
.. note::
This class requires that scikit-learn is installed.
"""
@classmethod
@HAS_SKLEARN.require_in_call
def _default_options(cls) -> Options:
"""Return default analysis options.
Analysis Options:
plot (bool): Set ``True`` to create figure for fit result.
plotter (BasePlotter): A plotter instance to visualize the analysis result.
ax (AxesSubplot): Optional. A matplotlib axis object in which to draw.
discriminator (BaseDiscriminator): The sklearn discriminator to classify the data.
The default is a quadratic discriminant analysis.
"""
options = super()._default_options()
options.plotter = IQPlotter(MplDrawer())
options.plotter.set_options(
discriminator_max_resolution=64,
style=PlotStyle(figsize=(6, 4), legend_loc=None),
)
options.plot = True
options.ax = None
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
options.discriminator = SkQDA(QuadraticDiscriminantAnalysis())
return options
@property
def plotter(self) -> BasePlotter:
"""A short-cut to the IQ plotter instance."""
return self._options.plotter
def _run_analysis(
self,
experiment_data: ExperimentData,
) -> Tuple[List[AnalysisResultData], List["matplotlib.figure.Figure"]]:
"""Train a discriminator based on the experiment data.
Args:
experiment_data: the data obtained from the experiment
Returns:
The configuration of the trained discriminator and the IQ plot and the fidelity of the
discrimination.
"""
# number of states and shots
n_states = len(experiment_data.data())
num_shots = len(experiment_data.data()[0]["memory"])
# Process the data and get labels
data, fit_state = [], []
for i in range(n_states):
state_data = []
for j in range(num_shots):
state_data.append(experiment_data.data()[i]["memory"][j][0])
data.append(np.array(state_data))
fit_state.append(experiment_data.data()[i]["metadata"]["label"])
# Train a discriminator on the processed data
discriminator = self.options.discriminator
discriminator.fit(
np.concatenate(data),
np.asarray([[label] * num_shots for label in fit_state]).flatten().transpose(),
)
# Calculate fidelity. First we need to calculate P(i|j):= prob. measuring outcome i given
# state j was prepared
predicted_data = [discriminator.predict(state_data) for state_data in data]
# count per prepared state the number of measured states of each kind and calculate the
# probability of measuring the wrong state
prob_wrong = 0
for i in range(n_states):
counts = [0] * n_states
for point in predicted_data[i]:
counts[point] += 1
for j in range(n_states):
if j != i:
prob_wrong += counts[j] / num_shots
# calculate the fidelity
fidelity = 1 - (1 / n_states) * prob_wrong
# Crate analysis results from the discriminator configuration
analysis_results = [
AnalysisResultData(name="discriminator_config", value=discriminator.config()),
AnalysisResultData(name="fidelity", value=fidelity),
]
figures = []
if self.options.plot:
figures.append(self._levels_plot(discriminator, data, fit_state, fidelity).get_figure())
return analysis_results, figures
def _levels_plot(self, discriminator, data, fit_state, fidelity) -> matplotlib.figure.Figure:
"""Helper function for plotting IQ plane for different energy levels.
Args:
discriminator: the trained discriminator
data: the training data
fit_state: the labels
fidelity: the fidelity of the classification
Returns:
The plotted IQ data.
"""
# create figure labels
params_dict = {}
for state in fit_state:
params_dict[state] = {"label": f"$|{state}\\rangle$"}
# Update params_dict to contain any existing series_params values,
# where they have priority over params_dict.
params_dict.update(self.plotter.figure_options.series_params)
self.plotter.set_figure_options(series_params=params_dict)
# calculate centroids
centroids = [np.mean(x, axis=0) for x in data]
for p, c, n in zip(data, centroids, fit_state):
self.plotter.set_series_data(n, points=p, centroid=c)
self.plotter.set_supplementary_data(discriminator=discriminator, fidelity=fidelity)
return self.plotter.figure()