phase_estimation

class qiskit.circuit.library.phase_estimation(num_evaluation_qubits, unitary, name='QPE')

Bases:

Phase Estimation circuit.

In the Quantum Phase Estimation (QPE) algorithm [1, 2, 3], the Phase Estimation circuit is used to estimate the phase $\phi$ of an eigenvalue $e^{2\pi i\phi}$ of a unitary operator $U$, provided with the corresponding eigenstate $|\psi\rangle$. That is

This estimation (and thereby this circuit) is a central routine to several well-known algorithms, such as Shor’s algorithm or Quantum Amplitude Estimation.

Parameters

• num_evaluation_qubits (int) – The number of evaluation qubits.
• unitary (QuantumCircuit) – The unitary operation $U$ which will be repeated and controlled.
• name (str) – The name of the circuit.

Return type

QuantumCircuit

Reference Circuit:

from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import phase_estimation
unitary = QuantumCircuit(2)
unitary.x(0)
unitary.y(1)
circuit = phase_estimation(3, unitary)
circuit.draw('mpl')

References:

[1]: Kitaev, A. Y. (1995). Quantum measurements and the Abelian Stabilizer Problem. 1–22.

quant-ph/9511026

[2]: Michael A. Nielsen and Isaac L. Chuang. 2011.

Quantum Computation and Quantum Information: 10th Anniversary Edition (10th ed.). Cambridge University Press, New York, NY, USA.

[3]: Qiskit

textbook