Quellcode für qiskit.circuit.library.phase_estimation

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# (C) Copyright IBM 2017, 2020.
# This code is licensed under the Apache License, Version 2.0. You may
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"""Phase estimation circuit."""

from typing import Optional

from qiskit.circuit import QuantumCircuit, QuantumRegister

from .basis_change import QFT

[Doku]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://learn.qiskit.org/course/ch-algorithms/quantum-phase-estimation>`_ """ 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: .. plot:: from qiskit.circuit import QuantumCircuit from qiskit.circuit.library import PhaseEstimation from qiskit.tools.jupyter.library import _generate_circuit_library_visualization unitary = QuantumCircuit(2) unitary.x(0) unitary.y(1) circuit = PhaseEstimation(3, unitary) _generate_circuit_library_visualization(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)