qiskit.aqua.algorithms.QAOA¶

class
QAOA
(operator=None, optimizer=None, p=1, initial_state=None, mixer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, aux_operators=None, callback=None, quantum_instance=None)[source]¶ The Quantum Approximate Optimization Algorithm.
QAOA is a wellknown algorithm for finding approximate solutions to combinatorialoptimization problems. The QAOA implementation in Aqua directly extends
VQE
and inherits VQE’s general hybrid optimization structure. However, unlike VQE, which can be configured with arbitrary variational forms, QAOA uses its own finetuned variational form, 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 variational form, 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 variational form.
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.
An initial state from Aqua’s
initial_states
may optionally be supplied. Parameters
operator (
Union
[OperatorBase
,LegacyBaseOperator
,None
]) – Qubit operatoroptimizer (
Optional
[Optimizer
]) – A classical optimizer.p (
int
) – the integer parameter p as specified in https://arxiv.org/abs/1411.4028, Has a minimum valid value of 1.initial_state (
Union
[QuantumCircuit
,InitialState
,None
]) – An optional initial state to prepend the QAOA circuit withmixer (
Union
[QuantumCircuit
,OperatorBase
,LegacyBaseOperator
,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 var_form 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.aux_operators (
Optional
[List
[Union
[OperatorBase
,LegacyBaseOperator
,None
]]]) – 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.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 variational form, the evaluated mean and the evaluated standard deviation.quantum_instance (
Union
[QuantumInstance
,Backend
,BaseBackend
,None
]) – Quantum Instance or Backend

__init__
(operator=None, optimizer=None, p=1, initial_state=None, mixer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, aux_operators=None, callback=None, quantum_instance=None)[source]¶  Parameters
operator (
Union
[OperatorBase
,LegacyBaseOperator
,None
]) – Qubit operatoroptimizer (
Optional
[Optimizer
]) – A classical optimizer.p (
int
) – the integer parameter p as specified in https://arxiv.org/abs/1411.4028, Has a minimum valid value of 1.initial_state (
Union
[QuantumCircuit
,InitialState
,None
]) – An optional initial state to prepend the QAOA circuit withmixer (
Union
[QuantumCircuit
,OperatorBase
,LegacyBaseOperator
,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 var_form 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.aux_operators (
Optional
[List
[Union
[OperatorBase
,LegacyBaseOperator
,None
]]]) – 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.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 variational form, the evaluated mean and the evaluated standard deviation.quantum_instance (
Union
[QuantumInstance
,Backend
,BaseBackend
,None
]) – Quantum Instance or Backend
Methods
__init__
([operator, optimizer, p, …]) type operator
Union
[OperatorBase
,LegacyBaseOperator
,None
]
set parameterized circuits to None
compute_minimum_eigenvalue
([operator, …])Computes minimum eigenvalue.
construct_circuit
(parameter)Return the circuits used to compute the expectation value.
construct_expectation
(parameter)Generate the ansatz circuit and expectation value measurement, and return their runnable composition.
find_minimum
([initial_point, var_form, …])Optimize to find the minimum cost value.
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.
run
([quantum_instance])Execute the algorithm with selected backend.
set_backend
(backend, **kwargs)Sets backend with configuration.
Whether computing the expectation value of auxiliary operators is supported.
Attributes
Returns aux operators
Returns backend.
The expectation value algorithm used to construct the expectation measurement from the observable.
Returns initial point
Returns: Returns the initial state.
Returns: Returns the mixer.
Returns operator
The optimal parameters for the variational form.
Returns optimizer
Returns quantum instance.
Return a numpy random.
Prepare the setting of VQE as a string.
Returns variational form

property
aux_operators
¶ Returns aux operators
 Return type
Optional
[List
[Optional
[OperatorBase
]]]

property
backend
¶ Returns backend.
 Return type
Union
[Backend
,BaseBackend
]

cleanup_parameterized_circuits
()¶ set parameterized circuits to None

compute_minimum_eigenvalue
(operator=None, 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.
 Parameters
operator (
Union
[OperatorBase
,LegacyBaseOperator
,None
]) – If not None replaces operator in algorithmaux_operators (
Optional
[List
[Union
[OperatorBase
,LegacyBaseOperator
,None
]]]) – If not None replaces aux_operators in algorithm
 Return type
MinimumEigensolverResult
 Returns
MinimumEigensolverResult

construct_circuit
(parameter)¶ Return the circuits used to compute the expectation value.
 Parameters
parameter (
Union
[List
[float
],List
[Parameter
],ndarray
]) – Parameters for the ansatz circuit. Return type
List
[QuantumCircuit
] Returns
A list of the circuits used to compute the expectation value.

construct_expectation
(parameter)¶ Generate the ansatz circuit and expectation value measurement, and return their runnable composition.
 Parameters
parameter (
Union
[List
[float
],List
[Parameter
],ndarray
]) – Parameters for the ansatz circuit. Return type
OperatorBase
 Returns
The Operator equalling the measurement of the ansatz
StateFn
by the Observable’s expectationStateFn
. Raises
AquaError – If no operator has been provided.

property
expectation
¶ The expectation value algorithm used to construct the expectation measurement from the observable.
 Return type
ExpectationBase

find_minimum
(initial_point=None, var_form=None, cost_fn=None, optimizer=None, gradient_fn=None)¶ Optimize to find the minimum cost value.
 Parameters
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.var_form (
Union
[QuantumCircuit
,VariationalForm
,None
]) – If not None will be used instead of any variational form 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
 Returns
Optimized variational parameters, and corresponding minimum cost value.
 Return type
dict
 Raises
ValueError – invalid input

get_optimal_circuit
()¶ Get the circuit with the optimal parameters.
 Return type
QuantumCircuit

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

get_optimal_vector
()¶ Get the simulation outcome of the optimal circuit.
 Return type
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
initial_point
¶ Returns initial point
 Return type
Optional
[ndarray
]

property
initial_state
¶ Returns: Returns the initial state.
 Return type
Union
[QuantumCircuit
,InitialState
,None
]

property
mixer
¶ Returns: Returns the mixer.
 Return type
Union
[QuantumCircuit
,OperatorBase
,LegacyBaseOperator
]

property
operator
¶ Returns operator
 Return type
Optional
[OperatorBase
]

property
optimal_params
¶ The optimal parameters for the variational form.
 Return type
List
[float
]

property
optimizer
¶ Returns optimizer
 Return type
Optional
[Optimizer
]

print_settings
()¶ Preparing the setting of VQE into a string.
 Returns
the formatted setting of VQE
 Return type
str

property
quantum_instance
¶ Returns quantum instance.
 Return type
Optional
[QuantumInstance
]

property
random
¶ Return a numpy random.

run
(quantum_instance=None, **kwargs)¶ Execute the algorithm with selected backend.
 Parameters
quantum_instance (
Union
[QuantumInstance
,Backend
,BaseBackend
,None
]) – the experimental setting.kwargs (dict) – kwargs
 Returns
results of an algorithm.
 Return type
dict
 Raises
AquaError – If a quantum instance or backend has not been provided

set_backend
(backend, **kwargs)¶ Sets backend with configuration.
 Return type
None

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.
 Return type
bool
 Returns
True if aux_operator expectations can be evaluated, False otherwise

property
var_form
¶ Returns variational form
 Return type
Union
[QuantumCircuit
,VariationalForm
,None
]