Source code for qiskit.algorithms.minimum_eigen_solvers.vqe

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# (C) Copyright IBM 2018, 2022.
# This code is licensed under the Apache License, Version 2.0. You may
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# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
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"""The Variational Quantum Eigensolver algorithm.

See https://arxiv.org/abs/1304.3061

from __future__ import annotations

import logging
import warnings
from time import time
from typing import Callable, Dict, List, Optional, Tuple, Union

import numpy as np

from qiskit.circuit import Parameter, QuantumCircuit
from qiskit.circuit.library import RealAmplitudes
from qiskit.opflow import (
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_function

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__)

[docs]class VQE(VariationalAlgorithm, MinimumEigensolver): r"""Pending deprecation: 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 The VQE class has been superseded by the :class:`qiskit.algorithms.minimum_eigensolvers.VQE` class.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_function( "The VQE class has been superseded by the " "qiskit.algorithms.minimum_eigensolvers.VQE class. " "This class will be deprecated in a future release and subsequently " "removed after that.", category=PendingDeprecationWarning, ) def __init__( self, ansatz: Optional[QuantumCircuit] = None, optimizer: Optional[Union[Optimizer, Minimizer]] = None, initial_point: Optional[np.ndarray] = None, gradient: Optional[Union[GradientBase, Callable]] = None, expectation: Optional[ExpectationBase] = None, include_custom: bool = False, max_evals_grouped: int = 1, callback: Optional[Callable[[int, np.ndarray, float, float], None]] = None, quantum_instance: Optional[Union[QuantumInstance, Backend]] = 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 = None # type: Optional[CircuitSampler] self._expectation = None self.expectation = expectation self._include_custom = include_custom self._ansatz = None self.ansatz = ansatz self._optimizer = None self.optimizer = optimizer self._initial_point = None self.initial_point = initial_point self._gradient = None self.gradient = gradient self._quantum_instance = None if quantum_instance is not None: self.quantum_instance = quantum_instance self._eval_time = None self._eval_count = 0 self._callback = None self.callback = callback logger.info(self.print_settings()) # TODO remove this once the stateful methods are deleted self._ret = None @property def ansatz(self) -> QuantumCircuit: """Returns the ansatz.""" return self._ansatz @ansatz.setter def ansatz(self, ansatz: Optional[QuantumCircuit]): """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) -> Optional[Union[GradientBase, Callable]]: """Returns the gradient.""" return self._gradient @gradient.setter def gradient(self, gradient: Optional[Union[GradientBase, Callable]]): """Sets the gradient.""" self._gradient = gradient @property def quantum_instance(self) -> Optional[QuantumInstance]: """Returns quantum instance.""" return self._quantum_instance @quantum_instance.setter def quantum_instance(self, quantum_instance: Union[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) -> Optional[np.ndarray]: """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) -> Optional[Callable[[int, np.ndarray, float, float], None]]: """Returns callback""" return self._callback @callback.setter def callback(self, callback: Optional[Callable[[int, np.ndarray, float, float], None]]): """Sets callback""" self._callback = callback @property def expectation(self) -> Optional[ExpectationBase]: """The expectation value algorithm used to construct the expectation measurement from the observable.""" return self._expectation @expectation.setter def expectation(self, exp: Optional[ExpectationBase]) -> 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: Optional[Optimizer]): """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
[docs] 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
[docs] def construct_expectation( self, parameter: Union[List[float], List[Parameter], np.ndarray], operator: OperatorBase, return_expectation: bool = False, ) -> Union[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
[docs] def construct_circuit( self, parameter: Union[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
[docs] @classmethod def supports_aux_operators(cls) -> bool: return True
[docs] def compute_minimum_eigenvalue( self, operator: OperatorBase, aux_operators: Optional[ListOrDict[OperatorBase]] = 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 = [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
[docs] def get_energy_evaluation( self, operator: OperatorBase, return_expectation: bool = False, ) -> Callable[[np.ndarray], Union[float, List[float]]]: """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) -> Union[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): """Pending deprecation: 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_function( "The VQEResult class has been superseded by the " "qiskit.algorithms.minimum_eigensolvers.VQEResult class. " "This class will be deprecated in a future release and subsequently " "removed after that.", category=PendingDeprecationWarning, ) def __init__(self) -> None: with warnings.catch_warnings(): warnings.simplefilter("ignore") super().__init__() self._cost_function_evals = None @property def cost_function_evals(self) -> Optional[int]: """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) -> Optional[np.ndarray]: """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