# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 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.
"""The Variational Quantum Eigensolver algorithm.
See https://arxiv.org/abs/1304.3061
"""
from __future__ import annotations
import logging
import warnings
from collections.abc import Callable
from time import time
import numpy as np
from qiskit.circuit import Parameter, QuantumCircuit
from qiskit.circuit.library import RealAmplitudes
from qiskit.opflow import (
CircuitSampler,
CircuitStateFn,
ExpectationBase,
ExpectationFactory,
ListOp,
OperatorBase,
PauliSumOp,
StateFn,
)
from qiskit.opflow.gradients import GradientBase
from qiskit.providers import Backend
from qiskit.utils import QuantumInstance, algorithm_globals
from qiskit.utils.backend_utils import is_aer_provider
from qiskit.utils.validation import validate_min
from qiskit.utils.deprecation import deprecate_func
from ..aux_ops_evaluator import eval_observables
from ..exceptions import AlgorithmError
from ..list_or_dict import ListOrDict
from ..optimizers import SLSQP, Minimizer, Optimizer
from ..variational_algorithm import VariationalAlgorithm, VariationalResult
from .minimum_eigen_solver import MinimumEigensolver, MinimumEigensolverResult
logger = logging.getLogger(__name__)
[documentos]class VQE(VariationalAlgorithm, MinimumEigensolver):
r"""Deprecated: Variational Quantum Eigensolver algorithm.
The VQE class has been superseded by the
:class:`qiskit.algorithms.minimum_eigensolvers.VQE` class.
This class will be deprecated in a future release and subsequently
removed after that.
`VQE <https://arxiv.org/abs/1304.3061>`__ is a quantum algorithm that uses a
variational technique to find
the minimum eigenvalue of the Hamiltonian :math:`H` of a given system.
An instance of VQE requires defining two algorithmic sub-components:
a trial state (a.k.a. ansatz) which is a :class:`QuantumCircuit`, and one of the classical
:mod:`~qiskit.algorithms.optimizers`. The ansatz is varied, via its set of parameters, by the
optimizer, such that it works towards a state, as determined by the parameters applied to the
ansatz, that will result in the minimum expectation value being measured of the input operator
(Hamiltonian).
An optional array of parameter values, via the *initial_point*, may be provided as the
starting point for the search of the minimum eigenvalue. This feature is particularly useful
such as when there are reasons to believe that the solution point is close to a particular
point. As an example, when building the dissociation profile of a molecule,
it is likely that using the previous computed optimal solution as the starting
initial point for the next interatomic distance is going to reduce the number of iterations
necessary for the variational algorithm to converge. It provides an
`initial point tutorial <https://github.com/Qiskit/qiskit-tutorials-community/blob/master
/chemistry/h2_vqe_initial_point.ipynb>`__ detailing this use case.
The length of the *initial_point* list value must match the number of the parameters
expected by the ansatz being used. If the *initial_point* is left at the default
of ``None``, then VQE will look to the ansatz for a preferred value, based on its
given initial state. If the ansatz returns ``None``,
then a random point will be generated within the parameter bounds set, as per above.
If the ansatz provides ``None`` as the lower bound, then VQE
will default it to :math:`-2\pi`; similarly, if the ansatz returns ``None``
as the upper bound, the default value will be :math:`2\pi`.
The optimizer can either be one of Qiskit's optimizers, such as
:class:`~qiskit.algorithms.optimizers.SPSA` or a callable with the following signature:
.. note::
The callable _must_ have the argument names ``fun, x0, jac, bounds`` as indicated
in the following code block.
.. 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 to directly pass 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")
"""
@deprecate_func(
additional_msg=(
"Instead, use the class ``qiskit.algorithms.minimum_eigensolvers.VQE``. "
"See https://qisk.it/algo_migration for a migration guide."
),
since="0.24.0",
)
def __init__(
self,
ansatz: QuantumCircuit | None = None,
optimizer: Optimizer | Minimizer | None = None,
initial_point: np.ndarray | None = None,
gradient: GradientBase | Callable | None = None,
expectation: ExpectationBase | None = None,
include_custom: bool = False,
max_evals_grouped: int = 1,
callback: Callable[[int, np.ndarray, float, float], None] | None = None,
quantum_instance: QuantumInstance | Backend | None = None,
) -> None:
"""
Args:
ansatz: A parameterized circuit used as Ansatz for the wave function.
optimizer: A classical optimizer. Can either be a Qiskit optimizer or a callable
that takes an array as input and returns a Qiskit or SciPy optimization result.
initial_point: An optional initial point (i.e. initial parameter values)
for the optimizer. If ``None`` then VQE will look to the ansatz for a preferred
point and if not will simply compute a random one.
gradient: An optional gradient function or operator for optimizer.
expectation: The Expectation converter for taking the average value of the
Observable over the ansatz state function. When ``None`` (the default) an
:class:`~qiskit.opflow.expectations.ExpectationFactory` is used to select
an appropriate expectation based on the operator and backend. When using Aer
qasm_simulator backend, with paulis, it is however much faster to leverage custom
Aer function for the computation but, although VQE performs much faster
with it, the outcome is ideal, with no shot noise, like using a state vector
simulator. If you are just looking for the quickest performance when choosing Aer
qasm_simulator and the lack of shot noise is not an issue then set `include_custom`
parameter here to ``True`` (defaults to ``False``).
include_custom: When `expectation` parameter here is None setting this to ``True`` will
allow the factory to include the custom Aer pauli expectation.
max_evals_grouped: Max number of evaluations performed simultaneously. Signals the
given optimizer that more than one set of parameters can be supplied so that
potentially the expectation values can be computed in parallel. Typically this is
possible when a finite difference gradient is used by the optimizer such that
multiple points to compute the gradient can be passed and if computed in parallel
improve overall execution time. Deprecated if a gradient operator or function is
given.
callback: a callback that can access the intermediate data during the optimization.
Four parameter values are passed to the callback as follows during each evaluation
by the optimizer for its current set of parameters as it works towards the minimum.
These are: the evaluation count, the optimizer parameters for the
ansatz, the evaluated mean and the evaluated standard deviation.`
quantum_instance: Quantum Instance or Backend
"""
validate_min("max_evals_grouped", max_evals_grouped, 1)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
super().__init__()
self._max_evals_grouped = max_evals_grouped
self._circuit_sampler: CircuitSampler | None = None
self._expectation = None
self.expectation = expectation
self._include_custom = include_custom
self._ansatz: QuantumCircuit | None = None
self.ansatz = ansatz
self._optimizer: Optimizer | None = None
self.optimizer = optimizer
self._initial_point: np.ndarray | None = None
self.initial_point = initial_point
self._gradient: GradientBase | Callable | None = None
self.gradient = gradient
self._quantum_instance: QuantumInstance | None = None
if quantum_instance is not None:
self.quantum_instance = quantum_instance
self._eval_time = None
self._eval_count = 0
self._callback: Callable[[int, np.ndarray, float, float], None] | None = None
self.callback = callback
logger.info(self.print_settings())
# TODO remove this once the stateful methods are deleted
self._ret: VQEResult | None = None
@property
def ansatz(self) -> QuantumCircuit:
"""Returns the ansatz."""
return self._ansatz
@ansatz.setter
def ansatz(self, ansatz: QuantumCircuit | None):
"""Sets the ansatz.
Args:
ansatz: The parameterized circuit used as an ansatz.
If None is passed, RealAmplitudes is used by default.
"""
if ansatz is None:
ansatz = RealAmplitudes()
self._ansatz = ansatz
@property
def gradient(self) -> GradientBase | Callable | None:
"""Returns the gradient."""
return self._gradient
@gradient.setter
def gradient(self, gradient: GradientBase | Callable | None):
"""Sets the gradient."""
self._gradient = gradient
@property
def quantum_instance(self) -> QuantumInstance | None:
"""Returns quantum instance."""
return self._quantum_instance
@quantum_instance.setter
def quantum_instance(self, quantum_instance: QuantumInstance | Backend) -> None:
"""Sets quantum_instance"""
if not isinstance(quantum_instance, QuantumInstance):
quantum_instance = QuantumInstance(quantum_instance)
self._quantum_instance = quantum_instance
self._circuit_sampler = CircuitSampler(
quantum_instance, param_qobj=is_aer_provider(quantum_instance.backend)
)
@property
def initial_point(self) -> np.ndarray | None:
"""Returns initial point"""
return self._initial_point
@initial_point.setter
def initial_point(self, initial_point: np.ndarray):
"""Sets initial point"""
self._initial_point = initial_point
@property
def max_evals_grouped(self) -> int:
"""Returns max_evals_grouped"""
return self._max_evals_grouped
@max_evals_grouped.setter
def max_evals_grouped(self, max_evals_grouped: int):
"""Sets max_evals_grouped"""
self._max_evals_grouped = max_evals_grouped
self.optimizer.set_max_evals_grouped(max_evals_grouped)
@property
def include_custom(self) -> bool:
"""Returns include_custom"""
return self._include_custom
@include_custom.setter
def include_custom(self, include_custom: bool):
"""Sets include_custom. If set to another value than the one that was previsously set,
the expectation attribute is reset to None.
"""
if include_custom != self._include_custom:
self._include_custom = include_custom
self.expectation = None
@property
def callback(self) -> Callable[[int, np.ndarray, float, float], None] | None:
"""Returns callback"""
return self._callback
@callback.setter
def callback(self, callback: Callable[[int, np.ndarray, float, float], None] | None):
"""Sets callback"""
self._callback = callback
@property
def expectation(self) -> ExpectationBase | None:
"""The expectation value algorithm used to construct the expectation measurement from
the observable."""
return self._expectation
@expectation.setter
def expectation(self, exp: ExpectationBase | None) -> None:
self._expectation = exp
def _check_operator_ansatz(self, operator: OperatorBase):
"""Check that the number of qubits of operator and ansatz match."""
if operator is not None and self.ansatz is not None:
if operator.num_qubits != self.ansatz.num_qubits:
# try to set the number of qubits on the ansatz, if possible
try:
self.ansatz.num_qubits = operator.num_qubits
except AttributeError as ex:
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 ex
@property
def optimizer(self) -> Optimizer:
"""Returns optimizer"""
return self._optimizer
@optimizer.setter
def optimizer(self, optimizer: Optimizer | None):
"""Sets the optimizer attribute.
Args:
optimizer: The optimizer to be used. If None is passed, SLSQP is used by default.
"""
if optimizer is None:
optimizer = SLSQP()
if isinstance(optimizer, Optimizer):
optimizer.set_max_evals_grouped(self.max_evals_grouped)
self._optimizer = optimizer
@property
def setting(self):
"""Prepare the setting of VQE as a string."""
ret = f"Algorithm: {self.__class__.__name__}\n"
params = ""
for key, value in self.__dict__.items():
if key[0] == "_":
if "initial_point" in key and value is None:
params += "-- {}: {}\n".format(key[1:], "Random seed")
else:
params += f"-- {key[1:]}: {value}\n"
ret += f"{params}"
return ret
[documentos] def print_settings(self):
"""
Preparing the setting of VQE into a string.
Returns:
str: the formatted setting of VQE
"""
ret = "\n"
ret += "==================== Setting of {} ============================\n".format(
self.__class__.__name__
)
ret += f"{self.setting}"
ret += "===============================================================\n"
if self.ansatz is not None:
ret += "{}".format(self.ansatz.draw(output="text"))
else:
ret += "ansatz has not been set"
ret += "===============================================================\n"
if callable(self.optimizer):
ret += "Optimizer is custom callable\n"
else:
ret += f"{self._optimizer.setting}"
ret += "===============================================================\n"
return ret
[documentos] def construct_expectation(
self,
parameter: list[float] | list[Parameter] | np.ndarray,
operator: OperatorBase,
return_expectation: bool = False,
) -> OperatorBase | tuple[OperatorBase, ExpectationBase]:
r"""
Generate the ansatz circuit and expectation value measurement, and return their
runnable composition.
Args:
parameter: Parameters for the ansatz circuit.
operator: Qubit operator of the Observable
return_expectation: If True, return the ``ExpectationBase`` expectation converter used
in the construction of the expectation value. Useful e.g. to compute the standard
deviation of the expectation value.
Returns:
The Operator equalling the measurement of the ansatz :class:`StateFn` by the
Observable's expectation :class:`StateFn`, and, optionally, the expectation converter.
Raises:
AlgorithmError: If no operator has been provided.
AlgorithmError: If no expectation is passed and None could be inferred via the
ExpectationFactory.
"""
if operator is None:
raise AlgorithmError("The operator was never provided.")
self._check_operator_ansatz(operator)
# if expectation was never created, try to create one
if self.expectation is None:
expectation = ExpectationFactory.build(
operator=operator,
backend=self.quantum_instance,
include_custom=self._include_custom,
)
else:
expectation = self.expectation
wave_function = self.ansatz.assign_parameters(parameter)
observable_meas = expectation.convert(StateFn(operator, is_measurement=True))
ansatz_circuit_op = CircuitStateFn(wave_function)
expect_op = observable_meas.compose(ansatz_circuit_op).reduce()
if return_expectation:
return expect_op, expectation
return expect_op
[documentos] def construct_circuit(
self,
parameter: list[float] | list[Parameter] | np.ndarray,
operator: OperatorBase,
) -> list[QuantumCircuit]:
"""Return the circuits used to compute the expectation value.
Args:
parameter: Parameters for the ansatz circuit.
operator: Qubit operator of the Observable
Returns:
A list of the circuits used to compute the expectation value.
"""
expect_op = self.construct_expectation(parameter, operator).to_circuit_op()
circuits = []
# recursively extract circuits
def extract_circuits(op):
if isinstance(op, CircuitStateFn):
circuits.append(op.primitive)
elif isinstance(op, ListOp):
for op_i in op.oplist:
extract_circuits(op_i)
extract_circuits(expect_op)
return circuits
[documentos] @classmethod
def supports_aux_operators(cls) -> bool:
return True
[documentos] def compute_minimum_eigenvalue(
self, operator: OperatorBase, aux_operators: ListOrDict[OperatorBase] | None = None
) -> MinimumEigensolverResult:
super().compute_minimum_eigenvalue(operator, aux_operators)
if self.quantum_instance is None:
raise AlgorithmError(
"A QuantumInstance or Backend must be supplied to run the quantum algorithm."
)
self.quantum_instance.circuit_summary = True
# this sets the size of the ansatz, so it must be called before the initial point
# validation
self._check_operator_ansatz(operator)
# set an expectation for this algorithm run (will be reset to None at the end)
initial_point = _validate_initial_point(self.initial_point, self.ansatz)
bounds = _validate_bounds(self.ansatz)
# We need to handle the array entries being zero or Optional i.e. having value None
if aux_operators:
zero_op = PauliSumOp.from_list([("I" * self.ansatz.num_qubits, 0)])
# Convert the None and zero values when aux_operators is a list.
# Drop None and convert zero values when aux_operators is a dict.
if isinstance(aux_operators, list):
key_op_iterator = enumerate(aux_operators)
converted: ListOrDict[OperatorBase] = [zero_op] * len(aux_operators)
else:
key_op_iterator = aux_operators.items()
converted = {}
for key, op in key_op_iterator:
if op is not None:
converted[key] = zero_op if op == 0 else op
aux_operators = converted
else:
aux_operators = None
# Convert the gradient operator into a callable function that is compatible with the
# optimization routine.
if isinstance(self._gradient, GradientBase):
gradient = self._gradient.gradient_wrapper(
~StateFn(operator) @ StateFn(self.ansatz),
bind_params=list(self.ansatz.parameters),
backend=self._quantum_instance,
)
else:
gradient = self._gradient
self._eval_count = 0
energy_evaluation, expectation = self.get_energy_evaluation(
operator, return_expectation=True
)
start_time = time()
if callable(self.optimizer):
opt_result = self.optimizer( # pylint: disable=not-callable
fun=energy_evaluation, x0=initial_point, jac=gradient, bounds=bounds
)
else:
opt_result = self.optimizer.minimize(
fun=energy_evaluation, x0=initial_point, jac=gradient, bounds=bounds
)
eval_time = time() - start_time
result = VQEResult()
result.optimal_point = opt_result.x
result.optimal_parameters = dict(zip(self.ansatz.parameters, opt_result.x))
result.optimal_value = opt_result.fun
result.cost_function_evals = opt_result.nfev
result.optimizer_time = eval_time
result.eigenvalue = opt_result.fun + 0j
result.eigenstate = self._get_eigenstate(result.optimal_parameters)
logger.info(
"Optimization complete in %s seconds.\nFound opt_params %s in %s evals",
eval_time,
result.optimal_point,
self._eval_count,
)
# TODO delete as soon as get_optimal_vector etc are removed
self._ret = result
if aux_operators is not None:
bound_ansatz = self.ansatz.bind_parameters(result.optimal_point)
aux_values = eval_observables(
self.quantum_instance, bound_ansatz, aux_operators, expectation=expectation
)
result.aux_operator_eigenvalues = aux_values
return result
[documentos] def get_energy_evaluation(
self,
operator: OperatorBase,
return_expectation: bool = False,
) -> Callable[[np.ndarray], float | list[float]] | tuple[
Callable[[np.ndarray], float | list[float]], ExpectationBase
]:
"""Returns a function handle to evaluates the energy at given parameters for the ansatz.
This is the objective function to be passed to the optimizer that is used for evaluation.
Args:
operator: The operator whose energy to evaluate.
return_expectation: If True, return the ``ExpectationBase`` expectation converter used
in the construction of the expectation value. Useful e.g. to evaluate other
operators with the same expectation value converter.
Returns:
Energy of the hamiltonian of each parameter, and, optionally, the expectation
converter.
Raises:
RuntimeError: If the circuit is not parameterized (i.e. has 0 free parameters).
"""
num_parameters = self.ansatz.num_parameters
if num_parameters == 0:
raise RuntimeError("The ansatz must be parameterized, but has 0 free parameters.")
ansatz_params = self.ansatz.parameters
expect_op, expectation = self.construct_expectation(
ansatz_params, operator, return_expectation=True
)
def energy_evaluation(parameters):
parameter_sets = np.reshape(parameters, (-1, num_parameters))
# Create dict associating each parameter with the lists of parameterization values for it
param_bindings = dict(zip(ansatz_params, parameter_sets.transpose().tolist()))
start_time = time()
sampled_expect_op = self._circuit_sampler.convert(expect_op, params=param_bindings)
means = np.real(sampled_expect_op.eval())
if self._callback is not None:
variance = np.real(expectation.compute_variance(sampled_expect_op))
estimator_error = np.sqrt(variance / self.quantum_instance.run_config.shots)
for i, param_set in enumerate(parameter_sets):
self._eval_count += 1
self._callback(self._eval_count, param_set, means[i], estimator_error[i])
else:
self._eval_count += len(means)
end_time = time()
logger.info(
"Energy evaluation returned %s - %.5f (ms), eval count: %s",
means,
(end_time - start_time) * 1000,
self._eval_count,
)
return means if len(means) > 1 else means[0]
if return_expectation:
return energy_evaluation, expectation
return energy_evaluation
def _get_eigenstate(self, optimal_parameters) -> list[float] | dict[str, int]:
"""Get the simulation outcome of the ansatz, provided with parameters."""
optimal_circuit = self.ansatz.bind_parameters(optimal_parameters)
state_fn = self._circuit_sampler.convert(StateFn(optimal_circuit)).eval()
if self.quantum_instance.is_statevector:
state = state_fn.primitive.data # VectorStateFn -> Statevector -> np.array
else:
state = state_fn.to_dict_fn().primitive # SparseVectorStateFn -> DictStateFn -> dict
return state
class VQEResult(VariationalResult, MinimumEigensolverResult):
"""Deprecated: VQE Result.
The VQEResult class has been superseded by the
:class:`qiskit.algorithms.minimum_eigensolvers.VQEResult` class.
This class will be deprecated in a future release and subsequently
removed after that.
"""
@deprecate_func(
additional_msg=(
"Instead, use the class ``qiskit.algorithms.minimum_eigensolvers.VQEResult``. "
"See https://qisk.it/algo_migration for a migration guide."
),
since="0.24.0",
)
def __init__(self) -> None:
with warnings.catch_warnings():
warnings.simplefilter("ignore")
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
@property
def eigenstate(self) -> np.ndarray | None:
"""return eigen state"""
return self._eigenstate
@eigenstate.setter
def eigenstate(self, value: np.ndarray) -> None:
"""set eigen state"""
self._eigenstate = value
def _validate_initial_point(point, ansatz):
expected_size = ansatz.num_parameters
# try getting the initial point from the ansatz
if point is None and hasattr(ansatz, "preferred_init_points"):
point = ansatz.preferred_init_points
# if the point is None choose a random initial point
if point is None:
# get bounds if ansatz has them set, otherwise use [-2pi, 2pi] for each parameter
bounds = getattr(ansatz, "parameter_bounds", None)
if bounds is None:
bounds = [(-2 * np.pi, 2 * np.pi)] * expected_size
# replace all Nones by [-2pi, 2pi]
lower_bounds = []
upper_bounds = []
for lower, upper in bounds:
lower_bounds.append(lower if lower is not None else -2 * np.pi)
upper_bounds.append(upper if upper is not None else 2 * np.pi)
# sample from within bounds
point = algorithm_globals.random.uniform(lower_bounds, upper_bounds)
elif len(point) != expected_size:
raise ValueError(
f"The dimension of the initial point ({len(point)}) does not match the "
f"number of parameters in the circuit ({expected_size})."
)
return point
def _validate_bounds(ansatz):
if hasattr(ansatz, "parameter_bounds") and ansatz.parameter_bounds is not None:
bounds = ansatz.parameter_bounds
if len(bounds) != ansatz.num_parameters:
raise ValueError(
f"The number of bounds ({len(bounds)}) does not match the number of "
f"parameters in the circuit ({ansatz.num_parameters})."
)
else:
bounds = [(None, None)] * ansatz.num_parameters
return bounds