qiskit.algorithms.QAOA¶

class
QAOA
(optimizer=None, reps=1, initial_state=None, mixer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, callback=None, quantum_instance=None)[Quellcode]¶ The Quantum Approximate Optimization Algorithm.
QAOA is a wellknown algorithm for finding approximate solutions to combinatorialoptimization problems.
The QAOA implementation directly extends
VQE
and inherits VQE’s optimization structure. However, unlike VQE, which can be configured with arbitrary ansatzes, QAOA uses its own finetuned ansatz, which comprises \(p\) parameterized global \(x\) rotations and \(p\) different parameterizations of the problem hamiltonian. QAOA is thus principally configured by the single integer parameter, p, which dictates the depth of the ansatz, and thus affects the approximation quality.An optional array of \(2p\) parameter values, as the initial_point, may be provided as the starting beta and gamma parameters (as identically named in the original QAOA paper) for the QAOA ansatz.
An operator or a parameterized quantum circuit may optionally also be provided as a custom mixer Hamiltonian. This allows, as discussed in this paper for quantum annealing, and in this paper for QAOA, to run constrained optimization problems where the mixer constrains the evolution to a feasible subspace of the full Hilbert space.
 Parameter
optimizer (
Optional
[Optimizer
]) – A classical optimizer.reps (
int
) – the integer parameter \(p\) as specified in https://arxiv.org/abs/1411.4028, Has a minimum valid value of 1.initial_state (
Optional
[QuantumCircuit
]) – An optional initial state to prepend the QAOA circuit withmixer (
Union
[QuantumCircuit
,OperatorBase
,None
]) – the mixer Hamiltonian to evolve with or a custom quantum circuit. Allows support of optimizations in constrained subspaces as per https://arxiv.org/abs/1709.03489 as well as warmstarting the optimization as introduced in http://arxiv.org/abs/2009.10095.initial_point (
Optional
[ndarray
]) – An optional initial point (i.e. initial parameter values) for the optimizer. IfNone
then it will simply compute a random one.gradient (
Union
[GradientBase
,Callable
[[Union
[ndarray
,List
]],List
],None
]) – An optional gradient operator respectively a gradient function used for optimization.expectation (
Optional
[ExpectationBase
]) – The Expectation converter for taking the average value of the Observable over the ansatz state function. When None (the default) anExpectationFactory
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. Ignored 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

__init__
(optimizer=None, reps=1, initial_state=None, mixer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, callback=None, quantum_instance=None)[Quellcode]¶  Parameter
optimizer (
Optional
[Optimizer
]) – A classical optimizer.reps (
int
) – the integer parameter \(p\) as specified in https://arxiv.org/abs/1411.4028, Has a minimum valid value of 1.initial_state (
Optional
[QuantumCircuit
]) – An optional initial state to prepend the QAOA circuit withmixer (
Union
[QuantumCircuit
,OperatorBase
,None
]) – the mixer Hamiltonian to evolve with or a custom quantum circuit. Allows support of optimizations in constrained subspaces as per https://arxiv.org/abs/1709.03489 as well as warmstarting the optimization as introduced in http://arxiv.org/abs/2009.10095.initial_point (
Optional
[ndarray
]) – An optional initial point (i.e. initial parameter values) for the optimizer. IfNone
then it will simply compute a random one.gradient (
Union
[GradientBase
,Callable
[[Union
[ndarray
,List
]],List
],None
]) – An optional gradient operator respectively a gradient function used for optimization.expectation (
Optional
[ExpectationBase
]) – The Expectation converter for taking the average value of the Observable over the ansatz state function. When None (the default) anExpectationFactory
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. Ignored 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
Methods
__init__
([optimizer, reps, initial_state, …]) type optimizer
Optional
[Optimizer
]
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.
get_prob_vector_for_params
(…[, …])Helper function to get probability vectors for a set of params
get_probabilities_for_counts
(counts)get probabilities for counts
Preparing the setting of VQE into a string.
Whether computing the expectation value of auxiliary operators is supported.
Attributes
Returns the ansatz.
The expectation value algorithm used to construct the expectation measurement from the observable.
Returns the gradient.
Returns initial point
Returns: Returns the initial state.
Returns: Returns the mixer.
The optimal parameters for the ansatz.
Returns optimizer
Returns quantum instance.
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)¶ 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 Observableaux_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)¶ 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)¶ 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 Observablereturn_expectation (
bool
) – If True, return theExpectationBase
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 expectationStateFn
, 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)¶ 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 theExpectationBase
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
()¶ Get the circuit with the optimal parameters.
 Rückgabetyp
QuantumCircuit

get_optimal_cost
()¶ Get the minimal cost or energy found by the VQE.
 Rückgabetyp
float

get_optimal_vector
()¶ 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
¶ Returns the gradient.
 Rückgabetyp
Union
[GradientBase
,Callable
,None
]

property
initial_point
¶ Returns initial point
 Rückgabetyp
Optional
[ndarray
]

property
initial_state
¶ Returns: Returns the initial state.
 Rückgabetyp
Optional
[QuantumCircuit
]

property
mixer
¶ Returns: Returns the mixer.
 Rückgabetyp
Union
[QuantumCircuit
,OperatorBase
]

property
optimal_params
¶ The optimal parameters for the ansatz.
 Rückgabetyp
ndarray

property
optimizer
¶ Returns optimizer
 Rückgabetyp
Optional
[Optimizer
]

print_settings
()¶ 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
()¶ 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