# This code is part of a Qiskit project.
#
# (C) Copyright IBM 2018, 2023.
#
# 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.
"""
ad hoc dataset
"""
from __future__ import annotations
import itertools as it
from functools import reduce
from typing import Tuple, Dict, List
import numpy as np
from qiskit.utils import optionals
from qiskit_algorithms.utils import algorithm_globals
from sklearn import preprocessing
[ドキュメント]def ad_hoc_data(
training_size: int,
test_size: int,
n: int,
gap: int,
plot_data: bool = False,
one_hot: bool = True,
include_sample_total: bool = False,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray] | Tuple[
np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray
]:
r"""Generates a toy dataset that can be fully separated with
:class:`~qiskit.circuit.library.ZZFeatureMap` according to the procedure
outlined in [1]. To construct the dataset, we first sample uniformly
distributed vectors :math:`\vec{x} \in (0, 2\pi]^{n}` and apply the
feature map
.. math::
|\Phi(\vec{x})\rangle = U_{{\Phi} (\vec{x})} H^{\otimes n} U_{{\Phi} (\vec{x})}
H^{\otimes n} |0^{\otimes n} \rangle
where
.. math::
U_{{\Phi} (\vec{x})} = \exp \left( i \sum_{S \subseteq [n] } \phi_S(\vec{x})
\prod_{i \in S} Z_i \right)
and
.. math::
\begin{cases}
\phi_{\{i, j\}} = (\pi - x_i)(\pi - x_j) \\
\phi_{\{i\}} = x_i
\end{cases}
We then attribute labels to the vectors according to the rule
.. math::
m(\vec{x}) = \begin{cases}
1 & \langle \Phi(\vec{x}) | V^\dagger \prod_i Z_i V | \Phi(\vec{x}) \rangle > \Delta \\
-1 & \langle \Phi(\vec{x}) | V^\dagger \prod_i Z_i V | \Phi(\vec{x}) \rangle < -\Delta
\end{cases}
where :math:`\Delta` is the separation gap, and
:math:`V\in \mathrm{SU}(4)` is a random unitary.
The current implementation only works with n = 2 or 3.
**References:**
[1] Havlíček V, Córcoles AD, Temme K, Harrow AW, Kandala A, Chow JM,
Gambetta JM. Supervised learning with quantum-enhanced feature
spaces. Nature. 2019 Mar;567(7747):209-12.
`arXiv:1804.11326 <https://arxiv.org/abs/1804.11326>`_
Args:
training_size: the number of training samples.
test_size: the number of testing samples.
n: number of qubits (dimension of the feature space). Must be 2 or 3.
gap: separation gap (:math:`\Delta`).
plot_data: whether to plot the data. Requires matplotlib.
one_hot: if True, return the data in one-hot format.
include_sample_total: if True, return all points in the uniform
grid in addition to training and testing samples.
Returns:
Training and testing samples.
Raises:
ValueError: if n is not 2 or 3.
"""
class_labels = [r"A", r"B"]
count = 0
if n == 2:
count = 100
elif n == 3:
count = 20 # coarseness of data separation
else:
raise ValueError(f"Supported values of 'n' are 2 and 3 only, but {n} is provided.")
# Define auxiliary matrices and initial state
z = np.diag([1, -1])
i_2 = np.eye(2)
h_2 = np.array([[1, 1], [1, -1]]) / np.sqrt(2)
h_n = reduce(np.kron, [h_2] * n)
psi_0 = np.ones(2**n) / np.sqrt(2**n)
# Generate Z matrices acting on each qubits
z_i = np.array([reduce(np.kron, [i_2] * i + [z] + [i_2] * (n - i - 1)) for i in range(n)])
# Construct the parity operator
bitstrings = ["".join(bstring) for bstring in it.product(*[["0", "1"]] * n)]
if n == 2:
bitstring_parity = [bstr.count("1") % 2 for bstr in bitstrings]
d_m = np.diag((-1) ** np.array(bitstring_parity))
elif n == 3:
bitstring_majority = [0 if bstr.count("0") > 1 else 1 for bstr in bitstrings]
d_m = np.diag((-1) ** np.array(bitstring_majority))
# Generate a random unitary operator by collecting eigenvectors of a
# random hermitian operator
basis = algorithm_globals.random.random(
(2**n, 2**n)
) + 1j * algorithm_globals.random.random((2**n, 2**n))
basis = np.array(basis).conj().T @ np.array(basis)
eigvals, eigvecs = np.linalg.eig(basis)
idx = eigvals.argsort()[::-1]
eigvecs = eigvecs[:, idx]
m_m = eigvecs.conj().T @ d_m @ eigvecs
# Generate a grid of points in the feature space and compute the
# expectation value of the parity
xvals = np.linspace(0, 2 * np.pi, count, endpoint=False)
ind_pairs = list(it.combinations(range(n), 2))
_sample_total = []
for x in it.product(*[xvals] * n):
x_arr = np.array(x)
phi = np.sum(x_arr[:, None, None] * z_i, axis=0)
phi += sum(
((np.pi - x_arr[i1]) * (np.pi - x_arr[i2]) * z_i[i1] @ z_i[i2] for i1, i2 in ind_pairs)
)
# u_u was actually scipy.linalg.expm(1j * phi), but this method is
# faster because phi is always a diagonal matrix.
# We first extract the diagonal elements, then do exponentiation, then
# construct a diagonal matrix from them.
u_u = np.diag(np.exp(1j * np.diag(phi)))
psi = u_u @ h_n @ u_u @ psi_0
exp_val = np.real(psi.conj().T @ m_m @ psi)
if np.abs(exp_val) > gap:
_sample_total.append(np.sign(exp_val))
else:
_sample_total.append(0)
sample_total = np.array(_sample_total).reshape(*[count] * n)
# Extract training and testing samples from grid
x_sample, y_sample = _sample_ad_hoc_data(sample_total, xvals, training_size + test_size, n)
if plot_data:
_plot_ad_hoc_data(x_sample, y_sample, training_size)
training_input = {
key: (x_sample[y_sample == k, :])[:training_size] for k, key in enumerate(class_labels)
}
test_input = {
key: (x_sample[y_sample == k, :])[training_size : (training_size + test_size)]
for k, key in enumerate(class_labels)
}
training_feature_array, training_label_array = _features_and_labels_transform(
training_input, class_labels, one_hot
)
test_feature_array, test_label_array = _features_and_labels_transform(
test_input, class_labels, one_hot
)
if include_sample_total:
return (
training_feature_array,
training_label_array,
test_feature_array,
test_label_array,
sample_total,
)
else:
return (
training_feature_array,
training_label_array,
test_feature_array,
test_label_array,
)
def _sample_ad_hoc_data(sample_total, xvals, num_samples, n):
count = sample_total.shape[0]
sample_a, sample_b = [], []
for i, sample_list in enumerate([sample_a, sample_b]):
label = 1 if i == 0 else -1
while len(sample_list) < num_samples:
draws = tuple(algorithm_globals.random.choice(count) for i in range(n))
if sample_total[draws] == label:
sample_list.append([xvals[d] for d in draws])
labels = np.array([0] * num_samples + [1] * num_samples)
samples = [sample_a, sample_b]
samples = np.reshape(samples, (2 * num_samples, n))
return samples, labels
@optionals.HAS_MATPLOTLIB.require_in_call
def _plot_ad_hoc_data(x_total, y_total, training_size):
import matplotlib.pyplot as plt
n = x_total.shape[1]
fig = plt.figure()
projection = "3d" if n == 3 else None
ax1 = fig.add_subplot(1, 1, 1, projection=projection)
for k in range(0, 2):
ax1.scatter(*x_total[y_total == k][:training_size].T)
ax1.set_title("Ad-hoc Data")
plt.show()
def _features_and_labels_transform(
dataset: Dict[str, np.ndarray], class_labels: List[str], one_hot: bool = True
) -> Tuple[np.ndarray, np.ndarray]:
"""
Converts a dataset into arrays of features and labels.
Args:
dataset: A dictionary in the format of {'A': numpy.ndarray, 'B': numpy.ndarray, ...}
class_labels: A list of classes in the dataset
one_hot (bool): if True - return one-hot encoded label
Returns:
A tuple of features as np.ndarray, label as np.ndarray
"""
features = np.concatenate(list(dataset.values()))
raw_labels = []
for category in dataset.keys():
num_samples = dataset[category].shape[0]
raw_labels += [category] * num_samples
if not raw_labels:
# no labels, empty dataset
labels = np.zeros((0, len(class_labels)))
return features, labels
if one_hot:
encoder = preprocessing.OneHotEncoder()
encoder.fit(np.array(class_labels).reshape(-1, 1))
labels = encoder.transform(np.array(raw_labels).reshape(-1, 1))
if not isinstance(labels, np.ndarray):
labels = np.array(labels.todense())
else:
encoder = preprocessing.LabelEncoder()
encoder.fit(np.array(class_labels))
labels = encoder.transform(np.array(raw_labels))
return features, labels