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Source code for qiskit.circuit.library.basis_change.qft

# 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.

"""Quantum Fourier Transform Circuit."""

from typing import Optional
import numpy as np

from qiskit.circuit import QuantumRegister

from ..blueprintcircuit import BlueprintCircuit

# pylint: disable=no-member


[docs]class QFT(BlueprintCircuit): r"""Quantum Fourier Transform Circuit. The Quantum Fourier Transform (QFT) on :math:`n` qubits is the operation .. math:: |j\rangle \mapsto \frac{1}{2^{n/2}} \sum_{k=0}^{2^n - 1} e^{2\pi ijk / 2^n} |k\rangle The circuit that implements this transformation can be implemented using Hadamard gates on each qubit, a series of controlled-U1 (or Z, depending on the phase) gates and a layer of Swap gates. The layer of Swap gates can in principle be dropped if the QFT appears at the end of the circuit, since then the re-ordering can be done classically. They can be turned off using the ``do_swaps`` attribute. For 4 qubits, the circuit that implements this transformation is: .. jupyter-execute:: :hide-code: from qiskit.circuit.library import QFT import qiskit.tools.jupyter circuit = QFT(4) %circuit_library_info circuit The inverse QFT can be obtained by calling the ``inverse`` method on this class. The respective circuit diagram is: .. jupyter-execute:: :hide-code: from qiskit.circuit.library import QFT import qiskit.tools.jupyter circuit = QFT(4).inverse() %circuit_library_info circuit One method to reduce circuit depth is to implement the QFT approximately by ignoring controlled-phase rotations where the angle is beneath a threshold. This is discussed in more detail in https://arxiv.org/abs/quant-ph/9601018 or https://arxiv.org/abs/quant-ph/0403071. Here, this can be adjusted using the ``approximation_degree`` attribute: the smallest ``approximation_degree`` rotation angles are dropped from the QFT. For instance, a QFT on 5 qubits with approximation degree 2 yields (the barriers are dropped in this example): .. jupyter-execute:: :hide-code: from qiskit.circuit.library import QFT import qiskit.tools.jupyter circuit = QFT(5, approximation_degree=2) %circuit_library_info circuit """
[docs] def __init__(self, num_qubits: Optional[int] = None, approximation_degree: int = 0, do_swaps: bool = True, inverse: bool = False, insert_barriers: bool = False, name: str = 'qft') -> None: """Construct a new QFT circuit. Args: num_qubits: The number of qubits on which the QFT acts. approximation_degree: The degree of approximation (0 for no approximation). do_swaps: Whether to include the final swaps in the QFT. inverse: If True, the inverse Fourier transform is constructed. insert_barriers: If True, barriers are inserted as visualization improvement. name: The name of the circuit. """ super().__init__(name=name) self._approximation_degree = approximation_degree self._do_swaps = do_swaps self._insert_barriers = insert_barriers self._inverse = inverse self._data = None self.num_qubits = num_qubits
@property def num_qubits(self) -> int: """The number of qubits in the QFT circuit. Returns: The number of qubits in the circuit. Note: This method needs to be overwritten to allow adding the setter for num_qubits while still complying to pylint. """ return super().num_qubits @num_qubits.setter def num_qubits(self, num_qubits: int) -> None: """Set the number of qubits. Note that this changes the registers of the circuit. Args: num_qubits: The new number of qubits. """ if num_qubits != self.num_qubits: self._invalidate() if num_qubits: self.qregs = [QuantumRegister(num_qubits, name='q')] else: self.qregs = [] @property def approximation_degree(self) -> int: """The approximation degree of the QFT. Returns: The currently set approximation degree. """ return self._approximation_degree @approximation_degree.setter def approximation_degree(self, approximation_degree: int) -> None: """Set the approximation degree of the QFT. Args: approximation_degree: The new approximation degree. Raises: ValueError: If the approximation degree is smaller than 0. """ if approximation_degree < 0: raise ValueError('Approximation degree cannot be smaller than 0.') if approximation_degree != self._approximation_degree: self._invalidate() self._approximation_degree = approximation_degree @property def insert_barriers(self) -> bool: """Whether barriers are inserted for better visualization or not. Returns: True, if barriers are inserted, False if not. """ return self._insert_barriers @insert_barriers.setter def insert_barriers(self, insert_barriers: bool) -> None: """Specify whether barriers are inserted for better visualization or not. Args: insert_barriers: If True, barriers are inserted, if False not. """ if insert_barriers != self._insert_barriers: self._invalidate() self._insert_barriers = insert_barriers @property def do_swaps(self) -> bool: """Whether the final swaps of the QFT are applied or not. Returns: True, if the final swaps are applied, False if not. """ return self._do_swaps @do_swaps.setter def do_swaps(self, do_swaps: bool) -> None: """Specifiy whether to do the final swaps of the QFT circuit or not. Args: do_swaps: If True, the final swaps are applied, if False not. """ if do_swaps != self._do_swaps: self._invalidate() self._do_swaps = do_swaps
[docs] def is_inverse(self) -> bool: """Whether the inverse Fourier transform is implemented. Returns: True, if the inverse Fourier transform is implemented, False otherwise. """ return self._inverse
def _invalidate(self) -> None: """Invalidate the current build of the circuit.""" self._data = None
[docs] def inverse(self) -> 'QFT': """Invert this circuit. Returns: The inverted circuit. """ if self.name in ('qft', 'iqft'): name = 'qft' if self._inverse else 'iqft' else: name = self.name + '_dg' inverted = self.copy(name=name) inverted._data = [] from qiskit.circuit.parametertable import ParameterTable inverted._parameter_table = ParameterTable() for inst, qargs, cargs in reversed(self._data): inverted._append(inst.inverse(), qargs, cargs) inverted._inverse = not self._inverse return inverted
def _swap_qubits(self): num_qubits = self.num_qubits for i in range(num_qubits // 2): self.swap(i, num_qubits - i - 1) def _check_configuration(self, raise_on_failure: bool = True) -> bool: valid = True if self.num_qubits is None: valid = False if raise_on_failure: raise AttributeError('The number of qubits has not been set.') return valid def _build(self) -> None: """Construct the circuit representing the desired state vector.""" super()._build() for j in range(self.num_qubits): self.h(j) num_entanglements = max(0, self.num_qubits - max(self.approximation_degree, j)) for k in range(j + 1, j + num_entanglements): lam = np.pi / (2 ** (k - j)) self.cp(lam, j, k) if self.insert_barriers: self.barrier() if self._do_swaps: self._swap_qubits() if self._inverse: self._data = super().inverse()

© Copyright 2020, Qiskit Development Team. Last updated on 2021/02/27.

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