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]¶ Bases:
qiskit.aqua.algorithms.amplitude_estimators.ae_algorithm.AmplitudeEstimationAlgorithmThe 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:quant-ph/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_circuits-1}] 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
Compute the alpha confidence interval using the method kind.
Construct the Amplitude Estimation w/o QPE quantum circuits.
Determine whether a given state is a good state.
Post processing of the raw amplitude estimation output \(0 \leq a \leq 1\).
Execute the algorithm with selected backend.
Sets backend with configuration.
Attributes
-
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/quant-ph/0005055) for more detail.
- Returns
the A operator as CircuitFactory
- Return type
-
backend¶ Returns backend.
- Return type
Union[Backend,BaseBackend]
-
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.
-
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/quant-ph/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
-
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.
-
q_factory¶ Get the Q operator, or Grover-operator 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/quant-ph/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
-
quantum_instance¶ Returns quantum instance.
- Return type
Optional[QuantumInstance]
-
random¶ Return a numpy random.
-
state_preparation¶ Get the \(\mathcal{A}\) operator encoding the amplitude \(a\).
- Return type
QuantumCircuit- Returns
The \(\mathcal{A}\) operator as QuantumCircuit.