# qiskit.algorithms.VQE¶

class VQE(ansatz=None, optimizer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, callback=None, quantum_instance=None, sort_parameters_by_name=None)[Quellcode]

The Variational Quantum Eigensolver algorithm.

VQE is a quantum algorithm that uses a variational technique to find the minimum eigenvalue of the Hamiltonian $$H$$ of a given system.

An instance of VQE requires defining two algorithmic sub-components: a trial state (a.k.a. ansatz) which is a QuantumCircuit, and one of the classical 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 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 $$-2\pi$$; similarly, if the ansatz returns None as the upper bound, the default value will be $$2\pi$$.

Parameter
• ansatz (Optional[QuantumCircuit]) – A parameterized circuit used as Ansatz for the wave function.

• optimizer (Optional[Optimizer]) – A classical optimizer.

• initial_point (Optional[ndarray]) – 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 (Union[GradientBase, Callable, None]) – An optional gradient function or operator for optimizer.

• expectation (Optional[ExpectationBase]) – The Expectation converter for taking the average value of the Observable over the ansatz state function. When None (the default) an 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 (bool) – When expectation parameter here is None setting this to True will allow the factory to include the custom Aer pauli expectation.

• max_evals_grouped (int) – 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 (Optional[Callable[[int, ndarray, float, float], None]]) – 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 (Union[QuantumInstance, BaseBackend, Backend, None]) – Quantum Instance or Backend

• sort_parameters_by_name (Optional[bool]) – Deprecated. If True, the initial point is bound to the ansatz parameters strictly sorted by name instead of the default circuit order. That means that the ansatz parameters are e.g. sorted as x[0] x[1] x[10] x[2] ... instead of x[0] x[1] x[2] ... x[10]. Set this to True to obtain the behavior prior to Qiskit Terra 0.18.0.

__init__(ansatz=None, optimizer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, callback=None, quantum_instance=None, sort_parameters_by_name=None)[Quellcode]
Parameter
• ansatz (Optional[QuantumCircuit]) – A parameterized circuit used as Ansatz for the wave function.

• optimizer (Optional[Optimizer]) – A classical optimizer.

• initial_point (Optional[ndarray]) – 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 (Union[GradientBase, Callable, None]) – An optional gradient function or operator for optimizer.

• expectation (Optional[ExpectationBase]) – The Expectation converter for taking the average value of the Observable over the ansatz state function. When None (the default) an 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 (bool) – When expectation parameter here is None setting this to True will allow the factory to include the custom Aer pauli expectation.

• max_evals_grouped (int) – 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 (Optional[Callable[[int, ndarray, float, float], None]]) – 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 (Union[QuantumInstance, BaseBackend, Backend, None]) – Quantum Instance or Backend

• sort_parameters_by_name (Optional[bool]) – Deprecated. If True, the initial point is bound to the ansatz parameters strictly sorted by name instead of the default circuit order. That means that the ansatz parameters are e.g. sorted as x[0] x[1] x[10] x[2] ... instead of x[0] x[1] x[2] ... x[10]. Set this to True to obtain the behavior prior to Qiskit Terra 0.18.0.

Methods

 __init__([ansatz, optimizer, initial_point, …]) type ansatz Optional[QuantumCircuit] set parameterized circuits to None compute_minimum_eigenvalue(operator[, …]) Computes minimum eigenvalue. construct_circuit(parameter, operator) Return the circuits used to compute the expectation value. construct_expectation(parameter, operator[, …]) Generate the ansatz circuit and expectation value measurement, and return their runnable composition. find_minimum([initial_point, ansatz, …]) Optimize to find the minimum cost value. get_energy_evaluation(operator[, …]) Returns a function handle to evaluates the energy at given parameters for the ansatz. Get the circuit with the optimal parameters. Get the minimal cost or energy found by the VQE. Get the simulation outcome of the optimal circuit. Helper function to get probability vectors for a set of params get probabilities for counts Preparing the setting of VQE into a string. Whether computing the expectation value of auxiliary operators is supported.

Attributes

 ansatz Returns the ansatz. expectation The expectation value algorithm used to construct the expectation measurement from the observable. gradient Returns the gradient. initial_point Returns initial point optimal_params The optimal parameters for the ansatz. optimizer Returns optimizer quantum_instance Returns quantum instance. setting Prepare the setting of VQE as a string.
property ansatz

Returns the ansatz.

Rückgabetyp

Optional[QuantumCircuit]

cleanup_parameterized_circuits()

set parameterized circuits to None

compute_minimum_eigenvalue(operator, aux_operators=None)[Quellcode]

Computes minimum eigenvalue. Operator and aux_operators can be supplied here and if not None will override any already set into algorithm so it can be reused with different operators. While an operator is required by algorithms, aux_operators are optional. To ‚remove‘ a previous aux_operators array use an empty list here.

Parameter
• operator (OperatorBase) – Qubit operator of the Observable

• aux_operators (Optional[List[Optional[OperatorBase]]]) – Optional list of auxiliary operators to be evaluated with the eigenstate of the minimum eigenvalue main result and their expectation values returned. For instance in chemistry these can be dipole operators, total particle count operators so we can get values for these at the ground state.

Rückgabetyp

MinimumEigensolverResult

Rückgabe

MinimumEigensolverResult

construct_circuit(parameter, operator)[Quellcode]

Return the circuits used to compute the expectation value.

Parameter
• parameter (Union[List[float], List[Parameter], ndarray]) – Parameters for the ansatz circuit.

• operator (OperatorBase) – Qubit operator of the Observable

Rückgabetyp

List[QuantumCircuit]

Rückgabe

A list of the circuits used to compute the expectation value.

construct_expectation(parameter, operator, return_expectation=False)[Quellcode]

Generate the ansatz circuit and expectation value measurement, and return their runnable composition.

Parameter
• parameter (Union[List[float], List[Parameter], ndarray]) – Parameters for the ansatz circuit.

• operator (OperatorBase) – Qubit operator of the Observable

• return_expectation (bool) – 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.

Rückgabetyp

Union[OperatorBase, Tuple[OperatorBase, ExpectationBase]]

Rückgabe

The Operator equalling the measurement of the ansatz StateFn by the Observable’s expectation StateFn, and, optionally, the expectation converter.

Verursacht
• AlgorithmError – If no operator has been provided.

• AlgorithmError – If no expectation is passed and None could be inferred via the ExpectationFactory.

property expectation

The expectation value algorithm used to construct the expectation measurement from the observable.

Rückgabetyp

Optional[ExpectationBase]

find_minimum(initial_point=None, ansatz=None, cost_fn=None, optimizer=None, gradient_fn=None)

Optimize to find the minimum cost value.

Parameter
• initial_point (Optional[ndarray]) – If not None will be used instead of any initial point supplied via constructor. If None and None was supplied to constructor then a random point will be used if the optimizer requires an initial point.

• ansatz (Optional[QuantumCircuit]) – If not None will be used instead of any ansatz supplied via constructor.

• cost_fn (Optional[Callable]) – If not None will be used instead of any cost_fn supplied via constructor.

• optimizer (Optional[Optimizer]) – If not None will be used instead of any optimizer supplied via constructor.

• gradient_fn (Optional[Callable]) – Optional gradient function for optimizer

Rückgabe

Optimized variational parameters, and corresponding minimum cost value.

Rückgabetyp

dict

Verursacht

ValueError – invalid input

get_energy_evaluation(operator, return_expectation=False)[Quellcode]

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.

Parameter
• operator (OperatorBase) – The operator whose energy to evaluate.

• return_expectation (bool) – 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.

Rückgabetyp

Callable[[ndarray], Union[float, List[float]]]

Rückgabe

Energy of the hamiltonian of each parameter, and, optionally, the expectation converter.

Verursacht

RuntimeError – If the circuit is not parameterized (i.e. has 0 free parameters).

get_optimal_circuit()[Quellcode]

Get the circuit with the optimal parameters.

Rückgabetyp

QuantumCircuit

get_optimal_cost()[Quellcode]

Get the minimal cost or energy found by the VQE.

Rückgabetyp

float

get_optimal_vector()[Quellcode]

Get the simulation outcome of the optimal circuit.

Rückgabetyp

Union[List[float], Dict[str, int]]

get_prob_vector_for_params(construct_circuit_fn, params_s, quantum_instance, construct_circuit_args=None)

Helper function to get probability vectors for a set of params

get_probabilities_for_counts(counts)

get probabilities for counts

property gradient

Rückgabetyp

Union[GradientBase, Callable, None]

property initial_point

Returns initial point

Rückgabetyp

Optional[ndarray]

property optimal_params

The optimal parameters for the ansatz.

Rückgabetyp

ndarray

property optimizer

Returns optimizer

Rückgabetyp

Optional[Optimizer]

print_settings()[Quellcode]

Preparing the setting of VQE into a string.

Rückgabe

the formatted setting of VQE

Rückgabetyp

str

property quantum_instance

Returns quantum instance.

Rückgabetyp

Optional[QuantumInstance]

property setting

Prepare the setting of VQE as a string.

classmethod supports_aux_operators()[Quellcode]

Whether computing the expectation value of auxiliary operators is supported.

If the minimum eigensolver computes an eigenstate of the main operator then it can compute the expectation value of the aux_operators for that state. Otherwise they will be ignored.

Rückgabetyp

bool

Rückgabe

True if aux_operator expectations can be evaluated, False otherwise