qiskit.aqua.algorithms.MaximumLikelihoodAmplitudeEstimation¶

class
MaximumLikelihoodAmplitudeEstimation
(num_oracle_circuits, state_preparation=None, grover_operator=None, objective_qubits=None, post_processing=None, a_factory=None, q_factory=None, i_objective=None, likelihood_evals=None, quantum_instance=None)[source]¶ The Maximum Likelihood Amplitude Estimation algorithm.
This class implements the quantum amplitude estimation (QAE) algorithm without phase estimation, as introduced in [1]. In comparison to the original QAE algorithm [2], this implementation relies solely on different powers of the Grover operator and does not require additional evaluation qubits. Finally, the estimate is determined via a maximum likelihood estimation, which is why this class in named
MaximumLikelihoodAmplitudeEstimation
.References
 [1]: Suzuki, Y., Uno, S., Raymond, R., Tanaka, T., Onodera, T., & Yamamoto, N. (2019).
Amplitude Estimation without Phase Estimation. arXiv:1904.10246.
 [2]: Brassard, G., Hoyer, P., Mosca, M., & Tapp, A. (2000).
Quantum Amplitude Amplification and Estimation. arXiv:quantph/0005055.
 Parameters
num_oracle_circuits (
int
) – The number of circuits applying different powers of the Grover oracle Q. The (num_oracle_circuits + 1) executed circuits will be [id, Q^2^0, …, Q^2^{num_oracle_circuits1}] A 0>, where A is the problem unitary encoded in the argument a_factory. Has a minimum value of 1.state_preparation (
Union
[QuantumCircuit
,CircuitFactory
,None
]) – A circuit preparing the input state, referred to as \(\mathcal{A}\).grover_operator (
Union
[QuantumCircuit
,CircuitFactory
,None
]) – The Grover operator \(\mathcal{Q}\) used as unitary in the phase estimation circuit.objective_qubits (
Optional
[List
[int
]]) – A list of qubit indices. A measurement outcome is classified as ‘good’ state if all objective qubits are in state \(1\rangle\), otherwise it is classified as ‘bad’.post_processing (
Optional
[Callable
[[float
],float
]]) – A mapping applied to the estimate of \(0 \leq a \leq 1\), usually used to map the estimate to a target interval.a_factory (
Optional
[CircuitFactory
]) – The CircuitFactory subclass object representing the problem unitary.q_factory (
Optional
[CircuitFactory
]) – The CircuitFactory subclass object representing. an amplitude estimation sample (based on a_factory)i_objective (
Optional
[int
]) – The index of the objective qubit, i.e. the qubit marking ‘good’ solutions with the state 1> and ‘bad’ solutions with the state 0>likelihood_evals (
Optional
[int
]) – The number of gridpoints for the maximum search of the likelihood functionquantum_instance (
Union
[QuantumInstance
,Backend
,BaseBackend
,None
]) – Quantum Instance or Backend

__init__
(num_oracle_circuits, state_preparation=None, grover_operator=None, objective_qubits=None, post_processing=None, a_factory=None, q_factory=None, i_objective=None, likelihood_evals=None, quantum_instance=None)[source]¶  Parameters
num_oracle_circuits (
int
) – The number of circuits applying different powers of the Grover oracle Q. The (num_oracle_circuits + 1) executed circuits will be [id, Q^2^0, …, Q^2^{num_oracle_circuits1}] A 0>, where A is the problem unitary encoded in the argument a_factory. Has a minimum value of 1.state_preparation (
Union
[QuantumCircuit
,CircuitFactory
,None
]) – A circuit preparing the input state, referred to as \(\mathcal{A}\).grover_operator (
Union
[QuantumCircuit
,CircuitFactory
,None
]) – The Grover operator \(\mathcal{Q}\) used as unitary in the phase estimation circuit.objective_qubits (
Optional
[List
[int
]]) – A list of qubit indices. A measurement outcome is classified as ‘good’ state if all objective qubits are in state \(1\rangle\), otherwise it is classified as ‘bad’.post_processing (
Optional
[Callable
[[float
],float
]]) – A mapping applied to the estimate of \(0 \leq a \leq 1\), usually used to map the estimate to a target interval.a_factory (
Optional
[CircuitFactory
]) – The CircuitFactory subclass object representing the problem unitary.q_factory (
Optional
[CircuitFactory
]) – The CircuitFactory subclass object representing. an amplitude estimation sample (based on a_factory)i_objective (
Optional
[int
]) – The index of the objective qubit, i.e. the qubit marking ‘good’ solutions with the state 1> and ‘bad’ solutions with the state 0>likelihood_evals (
Optional
[int
]) – The number of gridpoints for the maximum search of the likelihood functionquantum_instance (
Union
[QuantumInstance
,Backend
,BaseBackend
,None
]) – Quantum Instance or Backend
Methods
__init__
(num_oracle_circuits[, …]) type num_oracle_circuits
int
confidence_interval
(alpha[, kind])Compute the alpha confidence interval using the method kind.
construct_circuits
([measurement])Construct the Amplitude Estimation w/o QPE quantum circuits.
is_good_state
(measurement)Determine whether a given state is a good state.
post_processing
(value)Post processing of the raw amplitude estimation output \(0 \leq a \leq 1\).
run
([quantum_instance])Execute the algorithm with selected backend.
set_backend
(backend, **kwargs)Sets backend with configuration.
Attributes
Get the A operator encoding the amplitude a that’s approximated, i.e.
Returns backend.
Get the \(\mathcal{Q}\) operator, or Grover operator.
Get the index of the objective qubit.
Get the criterion for a measurement outcome to be in a ‘good’ state.
Get the Q operator, or Groveroperator for the Amplitude Estimation algorithm, i.e.
Returns quantum instance.
Return a numpy random.
Get the \(\mathcal{A}\) operator encoding the amplitude \(a\).

property
a_factory
¶ Get the A operator encoding the amplitude a that’s approximated, i.e.
A 0>_n 0> = sqrt{1  a} psi_0>_n 0> + sqrt{a} psi_1>_n 1>
see the original Brassard paper (https://arxiv.org/abs/quantph/0005055) for more detail.
 Returns
the A operator as CircuitFactory
 Return type

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

confidence_interval
(alpha, kind='fisher')[source]¶ Compute the alpha confidence interval using the method kind.
The confidence level is (1  alpha) and supported kinds are ‘fisher’, ‘likelihood_ratio’ and ‘observed_fisher’ with shorthand notations ‘fi’, ‘lr’ and ‘oi’, respectively.
 Parameters
alpha (
float
) – The confidence level.kind (
str
) – The method to compute the confidence interval. Defaults to ‘fisher’, which computes the theoretical Fisher information.
 Return type
List
[float
] Returns
The specified confidence interval.
 Raises
AquaError – If run() hasn’t been called yet.
NotImplementedError – If the method kind is not supported.

construct_circuits
(measurement=False)[source]¶ Construct the Amplitude Estimation w/o QPE quantum circuits.
 Parameters
measurement (
bool
) – Boolean flag to indicate if measurement should be included in the circuits. Return type
List
[QuantumCircuit
] Returns
A list with the QuantumCircuit objects for the algorithm.

property
grover_operator
¶ Get the \(\mathcal{Q}\) operator, or Grover operator.
If the Grover operator is not set, we try to build it from the \(\mathcal{A}\) operator and objective_qubits. This only works if objective_qubits is a list of integers.
 Return type
Optional
[QuantumCircuit
] Returns
The Grover operator, or None if neither the Grover operator nor the \(\mathcal{A}\) operator is set.

property
i_objective
¶ Get the index of the objective qubit. The objective qubit marks the psi_0> state (called ‘bad states’ in https://arxiv.org/abs/quantph/0005055) with 0> and psi_1> (‘good’ states) with 1>. If the A operator performs the mapping
A 0>_n 0> = sqrt{1  a} psi_0>_n 0> + sqrt{a} psi_1>_n 1>
then, the objective qubit is the last one (which is either 0> or 1>).
If the objective qubit (i_objective) is not set, we check if the Q operator (q_factory) is set and return the index specified there. If the q_factory is not defined, the index equals the number of qubits of the A operator (a_factory) minus one. If also the a_factory is not set, return None.
 Returns
the index of the objective qubit
 Return type
int

is_good_state
(measurement)¶ Determine whether a given state is a good state.
 Parameters
measurement (
str
) – A measurement as bitstring, e.g. ‘01100’. Return type
bool
 Returns
True if the measurement corresponds to a good state, False otherwise.
 Raises
ValueError – If
self.objective_qubits
is not set.

property
objective_qubits
¶ Get the criterion for a measurement outcome to be in a ‘good’ state.
 Return type
Optional
[List
[int
]] Returns
The criterion as list of qubit indices.

post_processing
(value)¶ Post processing of the raw amplitude estimation output \(0 \leq a \leq 1\).
 Parameters
value (
float
) – The estimation value \(a\). Return type
float
 Returns
The value after post processing, usually mapping the interval \([0, 1]\) to the target interval.

property
q_factory
¶ Get the Q operator, or Groveroperator for the Amplitude Estimation algorithm, i.e.
\[\mathcal{Q} = \mathcal{A} \mathcal{S}_0 \mathcal{A}^\dagger \mathcal{S}_f,\]where \(\mathcal{S}_0\) reflects about the 0>_n state and S_psi0 reflects about \(\Psi_0\rangle_n\). See https://arxiv.org/abs/quantph/0005055 for more detail.
If the Q operator is not set, we try to build it from the A operator. If neither the A operator is set, None is returned.
 Returns
returns the current Q factory of the algorithm
 Return type
QFactory

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
state_preparation
¶ Get the \(\mathcal{A}\) operator encoding the amplitude \(a\).
 Return type
QuantumCircuit
 Returns
The \(\mathcal{A}\) operator as QuantumCircuit.