# Source code for qiskit.circuit.library.phase_estimation

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""Phase estimation circuit."""
from typing import Optional
from qiskit.circuit import QuantumCircuit, QuantumRegister
from .basis_change import QFT
[docs]class PhaseEstimation(QuantumCircuit):
r"""Phase Estimation circuit.
In the Quantum Phase Estimation (QPE) algorithm [1, 2, 3], the Phase Estimation circuit is used
to estimate the phase :math:`\phi` of an eigenvalue :math:`e^{2\pi i\phi}` of a unitary operator
:math:`U`, provided with the corresponding eigenstate :math:`|psi\rangle`.
That is
.. math::
U|\psi\rangle = e^{2\pi i\phi} |\psi\rangle
This estimation (and thereby this circuit) is a central routine to several well-known
algorithms, such as Shor's algorithm or Quantum Amplitude Estimation.
**References:**
[1]: Kitaev, A. Y. (1995). Quantum measurements and the Abelian Stabilizer Problem. 1–22.
`quant-ph/9511026 <http://arxiv.org/abs/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 <https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html>`_
"""
def __init__(
self,
num_evaluation_qubits: int,
unitary: QuantumCircuit,
iqft: Optional[QuantumCircuit] = None,
name: str = "QPE",
) -> None:
"""
Args:
num_evaluation_qubits: The number of evaluation qubits.
unitary: The unitary operation :math:`U` which will be repeated and controlled.
iqft: A inverse Quantum Fourier Transform, per default the inverse of
:class:`~qiskit.circuit.library.QFT` is used. Note that the QFT should not include
the usual swaps!
name: The name of the circuit.
.. note::
The inverse QFT should not include a swap of the qubit order.
Reference Circuit:
.. jupyter-execute::
:hide-code:
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
import qiskit.tools.jupyter
unitary = QuantumCircuit(2)
unitary.x(0)
unitary.y(1)
circuit = PhaseEstimation(3, unitary)
%circuit_library_info circuit
"""
qr_eval = QuantumRegister(num_evaluation_qubits, "eval")
qr_state = QuantumRegister(unitary.num_qubits, "q")
circuit = QuantumCircuit(qr_eval, qr_state, name=name)
if iqft is None:
iqft = QFT(num_evaluation_qubits, inverse=True, do_swaps=False).reverse_bits()
circuit.h(qr_eval) # hadamards on evaluation qubits
for j in range(num_evaluation_qubits): # controlled powers
circuit.compose(unitary.power(2 ** j).control(), qubits=[j] + qr_state[:], inplace=True)
circuit.compose(iqft, qubits=qr_eval[:], inplace=True) # final QFT
super().__init__(*circuit.qregs, name=circuit.name)
self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)
```