# 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.
"""The Variational Quantum Eigensolver algorithm, optimized for diagonal Hamiltonians."""
from __future__ import annotations
from collections.abc import Callable
import logging
from time import time
from typing import Any
import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.primitives import BaseSampler
from qiskit.result import QuasiDistribution
from qiskit.quantum_info.operators.base_operator import BaseOperator
from ..exceptions import AlgorithmError
from ..list_or_dict import ListOrDict
from ..optimizers import Minimizer, Optimizer, OptimizerResult
from ..variational_algorithm import VariationalAlgorithm, VariationalResult
from .diagonal_estimator import _DiagonalEstimator
from .sampling_mes import (
SamplingMinimumEigensolver,
SamplingMinimumEigensolverResult,
)
from ..observables_evaluator import estimate_observables
from ..utils import validate_initial_point, validate_bounds
# private function as we expect this to be updated in the next released
from ..utils.set_batching import _set_default_batchsize
logger = logging.getLogger(__name__)
[docs]class SamplingVQE(VariationalAlgorithm, SamplingMinimumEigensolver):
r"""The Variational Quantum Eigensolver algorithm, optimized for diagonal Hamiltonians.
VQE is a hybrid quantum-classical algorithm that uses a variational technique to find the
minimum eigenvalue of a given diagonal Hamiltonian operator :math:`H_{\text{diag}}`.
In contrast to the :class:`~qiskit_algorithms.minimum_eigensolvers.VQE` class, the
``SamplingVQE`` algorithm is executed using a :attr:`sampler` primitive.
An instance of ``SamplingVQE`` also requires an :attr:`ansatz`, a parameterized
:class:`.QuantumCircuit`, to prepare the trial state :math:`|\psi(\vec\theta)\rangle`. It also
needs a classical :attr:`optimizer` which varies the circuit parameters :math:`\vec\theta` to
minimize the objective function, which depends on the chosen :attr:`aggregation`.
The optimizer can either be one of Qiskit's optimizers, such as
:class:`~qiskit_algorithms.optimizers.SPSA` or a callable with the following signature:
.. code-block:: python
from qiskit_algorithms.optimizers import OptimizerResult
def my_minimizer(fun, x0, jac=None, bounds=None) -> OptimizerResult:
# Note that the callable *must* have these argument names!
# Args:
# fun (callable): the function to minimize
# x0 (np.ndarray): the initial point for the optimization
# jac (callable, optional): the gradient of the objective function
# bounds (list, optional): a list of tuples specifying the parameter bounds
result = OptimizerResult()
result.x = # optimal parameters
result.fun = # optimal function value
return result
The above signature also allows one to use any SciPy minimizer, for instance as
.. code-block:: python
from functools import partial
from scipy.optimize import minimize
optimizer = partial(minimize, method="L-BFGS-B")
The following attributes can be set via the initializer but can also be read and updated once
the ``SamplingVQE`` object has been constructed.
Attributes:
sampler (BaseSampler): The sampler primitive to sample the circuits.
ansatz (QuantumCircuit): A parameterized quantum circuit to prepare the trial state.
optimizer (Optimizer | Minimizer): A classical optimizer to find the minimum energy. This
can either be an :class:`.Optimizer` or a callable implementing the
:class:`.Minimizer` protocol.
aggregation (float | Callable[[list[tuple[float, complex]], float] | None):
A float or callable to specify how the objective function evaluated on the basis states
should be aggregated. If a float, this specifies the :math:`\alpha \in [0,1]` parameter
for a CVaR expectation value [1]. If a callable, it takes a list of basis state
measurements specified as ``[(probability, objective_value)]`` and return an objective
value as float. If None, all an ordinary expectation value is calculated.
callback (Callable[[int, np.ndarray, float, dict[str, Any]], None] | None): A callback that
can access the intermediate data at each optimization step. These data are: the
evaluation count, the optimizer parameters for the ansatz, the evaluated value, and the
metadata dictionary.
References:
[1]: Barkoutsos, P. K., Nannicini, G., Robert, A., Tavernelli, I., and Woerner, S.,
"Improving Variational Quantum Optimization using CVaR"
`arXiv:1907.04769 <https://arxiv.org/abs/1907.04769>`_
"""
def __init__(
self,
sampler: BaseSampler,
ansatz: QuantumCircuit,
optimizer: Optimizer | Minimizer,
*,
initial_point: np.ndarray | None = None,
aggregation: float | Callable[[list[float]], float] | None = None,
callback: Callable[[int, np.ndarray, float, dict[str, Any]], None] | None = None,
) -> None:
r"""
Args:
sampler: The sampler primitive to sample the circuits.
ansatz: A parameterized quantum circuit to prepare the trial state.
optimizer: A classical optimizer to find the minimum energy. This can either be an
:class:`.Optimizer` or a callable implementing the :class:`.Minimizer` protocol.
initial_point: An optional initial point (i.e. initial parameter values) for the
optimizer. The length of the initial point must match the number of :attr:`ansatz`
parameters. If ``None``, a random point will be generated within certain parameter
bounds. ``SamplingVQE`` will look to the ansatz for these bounds. If the ansatz does
not specify bounds, bounds of :math:`-2\pi`, :math:`2\pi` will be used.
aggregation: A float or callable to specify how the objective function evaluated on the
basis states should be aggregated.
callback: A callback that can access the intermediate data at each optimization step.
These data are: the evaluation count, the optimizer parameters for the ansatz, the
estimated value, and the metadata dictionary.
"""
super().__init__()
self.sampler = sampler
self.ansatz = ansatz
self.optimizer = optimizer
self.aggregation = aggregation
self.callback = callback
# this has to go via getters and setters due to the VariationalAlgorithm interface
self._initial_point = initial_point
@property
def initial_point(self) -> np.ndarray | None:
"""Return the initial point."""
return self._initial_point
@initial_point.setter
def initial_point(self, value: np.ndarray | None) -> None:
"""Set the initial point."""
self._initial_point = value
def _check_operator_ansatz(self, operator: BaseOperator):
"""Check that the number of qubits of operator and ansatz match and that the ansatz is
parameterized.
"""
if operator.num_qubits != self.ansatz.num_qubits:
try:
logger.info(
"Trying to resize ansatz to match operator on %s qubits.", operator.num_qubits
)
self.ansatz.num_qubits = operator.num_qubits
except AttributeError as error:
raise AlgorithmError(
"The number of qubits of the ansatz does not match the "
"operator, and the ansatz does not allow setting the "
"number of qubits using `num_qubits`."
) from error
if self.ansatz.num_parameters == 0:
raise AlgorithmError("The ansatz must be parameterized, but has no free parameters.")
[docs] @classmethod
def supports_aux_operators(cls) -> bool:
return True
[docs] def compute_minimum_eigenvalue(
self,
operator: BaseOperator,
aux_operators: ListOrDict[BaseOperator] | None = None,
) -> SamplingMinimumEigensolverResult:
# check that the number of qubits of operator and ansatz match, and resize if possible
self._check_operator_ansatz(operator)
if len(self.ansatz.clbits) > 0:
self.ansatz.remove_final_measurements()
self.ansatz.measure_all()
initial_point = validate_initial_point(self.initial_point, self.ansatz)
bounds = validate_bounds(self.ansatz)
# NOTE: we type ignore below because the `return_best_measurement=True` is guaranteed to
# return a tuple
evaluate_energy, best_measurement = self._get_evaluate_energy( # type: ignore[misc]
operator, self.ansatz, return_best_measurement=True
)
start_time = time()
if callable(self.optimizer):
optimizer_result = self.optimizer(
fun=evaluate_energy, # type: ignore[arg-type]
x0=initial_point,
jac=None,
bounds=bounds,
)
else:
# we always want to submit as many estimations per job as possible for minimal
# overhead on the hardware
was_updated = _set_default_batchsize(self.optimizer)
optimizer_result = self.optimizer.minimize(
fun=evaluate_energy, # type: ignore[arg-type]
x0=initial_point,
bounds=bounds,
)
# reset to original value
if was_updated:
self.optimizer.set_max_evals_grouped(None)
optimizer_time = time() - start_time
logger.info(
"Optimization complete in %s seconds.\nFound opt_params %s.",
optimizer_time,
optimizer_result.x,
)
final_state = self.sampler.run([self.ansatz], [optimizer_result.x]).result().quasi_dists[0]
if aux_operators is not None:
aux_operators_evaluated = estimate_observables(
_DiagonalEstimator(sampler=self.sampler),
self.ansatz,
aux_operators,
optimizer_result.x, # type: ignore[arg-type]
)
else:
aux_operators_evaluated = None
return self._build_sampling_vqe_result(
self.ansatz.copy(),
optimizer_result,
aux_operators_evaluated, # type: ignore[arg-type]
best_measurement,
final_state,
optimizer_time,
)
def _get_evaluate_energy(
self,
operator: BaseOperator,
ansatz: QuantumCircuit,
return_best_measurement: bool = False,
) -> Callable[[np.ndarray], np.ndarray | float] | tuple[
Callable[[np.ndarray], np.ndarray | float], dict[str, Any]
]:
"""Returns a function handle to evaluate the energy at given parameters.
This is the objective function to be passed to the optimizer that is used for evaluation.
Args:
operator: The operator whose energy to evaluate.
ansatz: The ansatz preparing the quantum state.
return_best_measurement: If True, a handle to a dictionary containing the best
measurement evaluated with the cost function.
Returns:
A tuple of a callable evaluating the energy and (optionally) a dictionary containing the
best measurement of the energy evaluation.
Raises:
AlgorithmError: If the circuit is not parameterized (i.e. has 0 free parameters).
"""
num_parameters = ansatz.num_parameters
if num_parameters == 0:
raise AlgorithmError("The ansatz must be parameterized, but has 0 free parameters.")
# avoid creating an instance variable to remain stateless regarding results
eval_count = 0
best_measurement = {"best": None}
def store_best_measurement(best):
for best_i in best:
if best_measurement["best"] is None or _compare_measurements(
best_i, best_measurement["best"]
):
best_measurement["best"] = best_i
estimator = _DiagonalEstimator(
sampler=self.sampler,
callback=store_best_measurement,
aggregation=self.aggregation, # type: ignore[arg-type]
)
def evaluate_energy(parameters: np.ndarray) -> np.ndarray | float:
nonlocal eval_count
# handle broadcasting: ensure parameters is of shape [array, array, ...]
parameters = np.reshape(parameters, (-1, num_parameters)).tolist()
batch_size = len(parameters)
estimator_result = estimator.run(
batch_size * [ansatz], batch_size * [operator], parameters
).result()
values = estimator_result.values
if self.callback is not None:
metadata = estimator_result.metadata
for params, value, meta in zip(parameters, values, metadata):
eval_count += 1
self.callback(eval_count, params, value, meta)
result = values if len(values) > 1 else values[0]
return np.real(result)
if return_best_measurement:
return evaluate_energy, best_measurement
return evaluate_energy
def _build_sampling_vqe_result(
self,
ansatz: QuantumCircuit,
optimizer_result: OptimizerResult,
aux_operators_evaluated: ListOrDict[tuple[complex, tuple[complex, int]]],
best_measurement: dict[str, Any],
final_state: QuasiDistribution,
optimizer_time: float,
) -> SamplingVQEResult:
result = SamplingVQEResult()
result.eigenvalue = optimizer_result.fun
result.cost_function_evals = optimizer_result.nfev
result.optimal_point = optimizer_result.x # type: ignore[assignment]
result.optimal_parameters = dict(
zip(self.ansatz.parameters, optimizer_result.x) # type: ignore[arg-type]
)
result.optimal_value = optimizer_result.fun
result.optimizer_time = optimizer_time
result.aux_operators_evaluated = aux_operators_evaluated # type: ignore[assignment]
result.optimizer_result = optimizer_result
result.best_measurement = best_measurement["best"]
result.eigenstate = final_state
result.optimal_circuit = ansatz
return result
[docs]class SamplingVQEResult(VariationalResult, SamplingMinimumEigensolverResult):
"""The SamplingVQE Result."""
def __init__(self) -> None:
super().__init__()
self._cost_function_evals: int | None = None
@property
def cost_function_evals(self) -> int | None:
"""Returns number of cost optimizer evaluations"""
return self._cost_function_evals
@cost_function_evals.setter
def cost_function_evals(self, value: int) -> None:
"""Sets number of cost function evaluations"""
self._cost_function_evals = value
def _compare_measurements(candidate, current_best):
"""Compare two best measurements. Returns True if the candidate is better than current value.
This compares the following two criteria, in this precedence:
1. The smaller objective value is better
2. The higher probability for the objective value is better
"""
if candidate["value"] < current_best["value"]:
return True
elif candidate["value"] == current_best["value"]:
return candidate["probability"] > current_best["probability"]
return False