# 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 __future__ import annotations from qiskit.circuit import QuantumCircuit, QuantumRegister, Gate from qiskit.utils.deprecation import deprecate_func from qiskit.circuit.library import QFT 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 `_ [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 `_ """ @deprecate_func( since="2.1", additional_msg="Use qiskit.circuit.library.phase_estimation instead.", removal_timeline="in Qiskit 3.0", ) def __init__( self, num_evaluation_qubits: int, unitary: QuantumCircuit, iqft: QuantumCircuit | None = 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:: :alt: Diagram illustrating the previously described circuit. from qiskit.circuit import QuantumCircuit from qiskit.circuit.library import PhaseEstimation from qiskit.visualization.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) def phase_estimation( num_evaluation_qubits: int, unitary: QuantumCircuit | Gate, name: str = "QPE", ) -> 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. Args: num_evaluation_qubits: The number of evaluation qubits. unitary: The unitary operation :math:`U` which will be repeated and controlled. This can either be a :class:`.QuantumCircuit` or a :class:`.Gate`. Passing gates can often be more performant, as it allows calling optimized control and power subroutines. name: The name of the output circuit. Reference Circuit: .. plot:: :alt: A phase estimation circuit. :include-source: from qiskit.circuit.library import phase_estimation, PauliEvolutionGate from qiskit.quantum_info import SparsePauliOp hamiltonian = SparsePauliOp(["ZZ", "IX", "XI"]) evo = PauliEvolutionGate(hamiltonian, time=0.1) # implements exp(-itH) circuit = phase_estimation(3, evo) # QPE for the evolution operator 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 `_ """ # pylint: disable=cyclic-import from qiskit.circuit.library import PermutationGate, QFTGate qr_eval = QuantumRegister(num_evaluation_qubits, "eval") qr_state = QuantumRegister(unitary.num_qubits, "q") circuit = QuantumCircuit(qr_eval, qr_state, name=name) 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.append(QFTGate(num_evaluation_qubits).inverse(), qr_eval[:]) reversal_pattern = list(reversed(range(num_evaluation_qubits))) circuit.append(PermutationGate(reversal_pattern), qr_eval[:]) return circuit