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QFT

QuICT.algorithm.qft.QFT 

QFT(targets: int, with_swap: bool = False, name: str = 'QFT')

Bases: CompositeGate

Implement the Quantum Fourier Transform without the swap gates.

\[ \vert{j}\rangle \mapsto \frac{1}{2^{n/2}} \bigotimes_{l=n}^{1}[\vert{0}\rangle + e^{2\pi ij2^{-l}}\vert{1}\rangle] \]
Reference

Nielsen, M.A., & Chuang, I.L. (2010). Quantum Computation and Quantum Information (10th Anniversary edition).

Examples:

from QuICT.core import Circuit
from QuICT.algorithm.qft import QFT

circuit = Circuit(3)
QFT(3) | circuit
circuit.draw(method="command", flatten=True)

        ┌───┐┌─────┐┌─────┐
q_0: |0>┤ h ├┤ cu1 ├┤ cu1 ├─────────────────
        └───┘└──┬──┘└──┬──┘┌───┐┌─────┐
q_1: |0>────────■──────┼───┤ h ├┤ cu1 ├─────
                       │   └───┘└──┬──┘┌───┐
q_2: |0>───────────────■───────────■───┤ h ├
                                       └───┘

Parameters:

  • targets (int) –

    The qubits' number.

  • with_swap (bool, default: False ) –

    If True, will include the swap gates in QFT.

  • name (str, default: 'QFT' ) –

    Name of the QFT gate.

Raises: GateParametersAssignedError: If targets is smaller than 2.

Source code in QuICT/algorithm/qft/quantum_frourier_transform.py 
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def __init__(self, targets: int, with_swap: bool = False, name: str = "QFT"):
    """
    Args:
        targets (int): The qubits' number.
        with_swap (bool): If `True`, will include the swap gates in QFT.
        name (str, optional): Name of the QFT gate.
    Raises:
        GateParametersAssignedError: If `targets` is smaller than 2.
    """
    if targets < 2:
        raise GateParametersAssignedError("QFT Gate needs at least two target qubits.")

    self.with_swap = with_swap

    super().__init__(name)

    self._qft_build(targets)

    if with_swap:
        for i in range(targets // 2):
            Swap | self([i, targets - 1 - i])

QuICT.algorithm.qft.IQFT 

IQFT(targets: int, with_swap: bool = False, name: str = 'IQFT')

Bases: CompositeGate

Implement inverse of the Quantum Fourier Transform without the swap gates.

\[ \frac{1}{2^{n/2}} \bigotimes_{l=n}^{1}[\vert{0}\rangle + e^{2\pi ij2^{-l}}\vert{1}\rangle] \mapsto \vert{j}\rangle \]

Examples:

from QuICT.core import Circuit
from QuICT.algorithm.qft import IQFT

circuit = Circuit(3)
IQFT(3) | circuit
circuit.draw(method="command", flatten=True)

                         ┌─────┐┌─────┐┌───┐
q_0: |0>─────────────────┤ cu1 ├┤ cu1 ├┤ h ├
             ┌─────┐┌───┐└──┬──┘└──┬──┘└───┘
q_1: |0>─────┤ cu1 ├┤ h ├───┼──────■────────
        ┌───┐└──┬──┘└───┘   │
q_2: |0>┤ h ├───■───────────■───────────────
        └───┘

Parameters:

  • targets (int) –

    The qubits' number.

  • with_swap (bool, default: False ) –

    If True, will include the swap gates in IQFT.

  • name (str, default: 'IQFT' ) –

    Name of the IQFT gate.

Raises: GateParametersAssignedError: If targets is smaller than 2.

Source code in QuICT/algorithm/qft/quantum_frourier_transform.py 
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def __init__(self, targets: int, with_swap: bool = False, name: str = "IQFT"):
    """
    Args:
        targets (int): The qubits' number.
        with_swap (bool): If `True`, will include the swap gates in IQFT.
        name (str, optional): Name of the IQFT gate.
    Raises:
        GateParametersAssignedError: If `targets` is smaller than 2.
    """
    if targets < 2:
        raise GateParametersAssignedError("IQFT Gate needs at least two target qubits.")

    self.with_swap = with_swap

    super().__init__(name)

    if with_swap:
        for i in range(targets // 2):
            Swap | self([i, targets - 1 - i])

    self._iqft_build(targets)