# This code is part of a Qiskit project.
#
# (C) Copyright IBM 2022, 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.
"""Gradient of Sampler with Finite difference method."""
from __future__ import annotations
from collections import defaultdict
from collections.abc import Sequence
import numpy as np
from qiskit.circuit import Parameter, QuantumCircuit
from qiskit.primitives import BaseSampler
from qiskit.providers import Options
from ..base.base_sampler_gradient import BaseSamplerGradient
from ..base.sampler_gradient_result import SamplerGradientResult
from ...exceptions import AlgorithmError
[docs]class SPSASamplerGradient(BaseSamplerGradient):
"""
Compute the gradients of the sampling probability by the Simultaneous Perturbation Stochastic
Approximation (SPSA) [1].
**Reference:**
[1] J. C. Spall, Adaptive stochastic approximation by the simultaneous perturbation method in
IEEE Transactions on Automatic Control, vol. 45, no. 10, pp. 1839-1853, Oct 2020,
`doi: 10.1109/TAC.2000.880982 <https://ieeexplore.ieee.org/document/880982>`_.
"""
def __init__(
self,
sampler: BaseSampler,
epsilon: float,
batch_size: int = 1,
seed: int | None = None,
options: Options | None = None,
):
"""
Args:
sampler: The sampler used to compute the gradients.
epsilon: The offset size for the SPSA gradients.
batch_size: number of gradients to average.
seed: The seed for a random perturbation vector.
options: Primitive backend runtime options used for circuit execution.
The order of priority is: options in ``run`` method > gradient's
default options > primitive's default setting.
Higher priority setting overrides lower priority setting
Raises:
ValueError: If ``epsilon`` is not positive.
"""
if epsilon <= 0:
raise ValueError(f"epsilon ({epsilon}) should be positive.")
self._batch_size = batch_size
self._epsilon = epsilon
self._seed = np.random.default_rng(seed)
super().__init__(sampler, options)
def _run(
self,
circuits: Sequence[QuantumCircuit],
parameter_values: Sequence[Sequence[float]],
parameters: Sequence[Sequence[Parameter]],
**options,
) -> SamplerGradientResult:
"""Compute the sampler gradients on the given circuits."""
job_circuits, job_param_values, metadata, offsets = [], [], [], []
all_n = []
for circuit, parameter_values_, parameters_ in zip(circuits, parameter_values, parameters):
# Indices of parameters to be differentiated.
indices = [circuit.parameters.data.index(p) for p in parameters_]
metadata.append({"parameters": parameters_})
offset = np.array(
[
(-1) ** (self._seed.integers(0, 2, len(circuit.parameters)))
for _ in range(self._batch_size)
]
)
plus = [parameter_values_ + self._epsilon * offset_ for offset_ in offset]
minus = [parameter_values_ - self._epsilon * offset_ for offset_ in offset]
offsets.append(offset)
# Combine inputs into a single job to reduce overhead.
n = 2 * self._batch_size
job_circuits.extend([circuit] * n)
job_param_values.extend(plus + minus)
all_n.append(n)
# Run the single job with all circuits.
job = self._sampler.run(job_circuits, job_param_values, **options)
try:
results = job.result()
except Exception as exc:
raise AlgorithmError("Sampler job failed.") from exc
# Compute the gradients.
gradients = []
partial_sum_n = 0
for i, n in enumerate(all_n):
dist_diffs = {}
result = results.quasi_dists[partial_sum_n : partial_sum_n + n]
for j, (dist_plus, dist_minus) in enumerate(zip(result[: n // 2], result[n // 2 :])):
dist_diff: dict[int, float] = defaultdict(float)
for key, value in dist_plus.items():
dist_diff[key] += value / (2 * self._epsilon)
for key, value in dist_minus.items():
dist_diff[key] -= value / (2 * self._epsilon)
dist_diffs[j] = dist_diff
gradient = []
indices = [circuits[i].parameters.data.index(p) for p in metadata[i]["parameters"]]
for j in indices:
gradient_j: dict[int, float] = defaultdict(float)
for k in range(self._batch_size):
for key, value in dist_diffs[k].items():
gradient_j[key] += value * offsets[i][k][j]
gradient_j = {key: value / self._batch_size for key, value in gradient_j.items()}
gradient.append(gradient_j)
gradients.append(gradient)
partial_sum_n += n
opt = self._get_local_options(options)
return SamplerGradientResult(gradients=gradients, metadata=metadata, options=opt)