MaximumLikelihoodAmplitudeEstimation

class MaximumLikelihoodAmplitudeEstimation(num_oracle_circuits, a_factory=None, q_factory=None, i_objective=None, likelihood_evals=None, quantum_instance=None)

The Maximum Likelihood Amplitude Estimation algorithm.

This class implements the an quantum amplitude estimation (QAE) algorithm without phase estimation, according to https://arxiv.org/abs/1904.10246. In comparison to the original QAE algorithm (https://arxiv.org/abs/quant-ph/0005055), this implementation relies solely on different powers of the Grover algorithm and does not require ancilla qubits. Finally, the estimate is determined via a maximum likelihood estimation, which is why this class in named MaximumLikelihoodAmplitudeEstimation.

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.

• 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 function

• quantum_instance (Union[QuantumInstance, BaseBackend, None]) – Quantum Instance or Backend

Attributes

MaximumLikelihoodAmplitudeEstimation.a_factory	Get the A operator encoding the amplitude a that’s approximated, i.e.
MaximumLikelihoodAmplitudeEstimation.backend	Returns backend.
MaximumLikelihoodAmplitudeEstimation.i_objective	Get the index of the objective qubit.
MaximumLikelihoodAmplitudeEstimation.q_factory	Get the Q operator, or Grover-operator for the Amplitude Estimation algorithm, i.e.
MaximumLikelihoodAmplitudeEstimation.quantum_instance	Returns quantum instance.
MaximumLikelihoodAmplitudeEstimation.random	Return a numpy random.

Methods

MaximumLikelihoodAmplitudeEstimation.confidence_interval(alpha)	Compute the alpha confidence interval using the method kind.
MaximumLikelihoodAmplitudeEstimation.construct_circuits([…])	Construct the Amplitude Estimation w/o QPE quantum circuits.
MaximumLikelihoodAmplitudeEstimation.run([…])	Execute the algorithm with selected backend.
MaximumLikelihoodAmplitudeEstimation.set_backend(…)	Sets backend with configuration.