# IterativePhaseEstimation#

class IterativePhaseEstimation(num_iterations, sampler=None)[source]#

Bases: PhaseEstimator

Run the Iterative quantum phase estimation (QPE) algorithm.

Given a unitary circuit and a circuit preparing an eigenstate, return the phase of the eigenvalue as a number in $$[0,1)$$ using the iterative phase estimation algorithm.

[1]: Dobsicek et al. (2006), Arbitrary accuracy iterative phase estimation algorithm as a two

qubit benchmark, arxiv/quant-ph/0610214

Parameters:
• num_iterations (int) – The number of iterations (rounds) of the phase estimation to run.

• sampler (BaseSampler | None) – The sampler primitive on which the circuit will be sampled.

Raises:

Methods

construct_circuit(unitary, state_preparation, k, omega=0.0, measurement=False)[source]#

Construct the kth iteration Quantum Phase Estimation circuit.

For details of parameters, see Fig. 2 in https://arxiv.org/pdf/quant-ph/0610214.pdf.

Parameters:
• unitary (QuantumCircuit) – The circuit representing the unitary operator whose eigenvalue (via phase) will be measured.

• state_preparation (QuantumCircuit) – The circuit that prepares the state whose eigenphase will be measured. If this parameter is omitted, no preparation circuit will be run and input state will be the all-zero state in the computational basis.

• k (int) – the iteration idx.

• omega (float) – the feedback angle.

• measurement (bool) – Boolean flag to indicate if measurement should be included in the circuit.

Returns:

the quantum circuit per iteration

Return type:

QuantumCircuit

estimate(unitary, state_preparation)[source]#

Estimate the eigenphase of the input unitary and initial-state pair.

Parameters:
• unitary (QuantumCircuit) – The circuit representing the unitary operator whose eigenvalue (via phase) will be measured.

• state_preparation (QuantumCircuit) – The circuit that prepares the state whose eigenphase will be measured. If this parameter is omitted, no preparation circuit will be run and input state will be the all-zero state in the computational basis.

Returns:

Estimated phase in an IterativePhaseEstimationResult object.

Raises:

AlgorithmError – If a sampler is not provided.

Return type:

IterativePhaseEstimationResult