# This code is part of Qiskit.
#
# (C) Copyright IBM 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.
"""Implementations of boolean logic quantum circuits."""
from __future__ import annotations
from qiskit.circuit import QuantumRegister, QuantumCircuit, AncillaRegister
from qiskit.circuit.library.standard_gates import MCXGate
[Doku]class AND(QuantumCircuit):
r"""A circuit implementing the logical AND operation on a number of qubits.
For the AND operation the state :math:`|1\rangle` is interpreted as ``True``. The result
qubit is flipped, if the state of all variable qubits is ``True``. In this format, the AND
operation equals a multi-controlled X gate, which is controlled on all variable qubits.
Using a list of flags however, qubits can be skipped or negated. Practically, the flags
allow to skip controls or to apply pre- and post-X gates to the negated qubits.
The AND gate without special flags equals the multi-controlled-X gate:
.. plot::
from qiskit.circuit.library import AND
from qiskit.tools.jupyter.library import _generate_circuit_library_visualization
circuit = AND(5)
_generate_circuit_library_visualization(circuit)
Using flags we can negate qubits or skip them. For instance, if we have 5 qubits and want to
return ``True`` if the first qubit is ``False`` and the last two are ``True`` we use the flags
``[-1, 0, 0, 1, 1]``.
.. plot::
from qiskit.circuit.library import AND
from qiskit.tools.jupyter.library import _generate_circuit_library_visualization
circuit = AND(5, flags=[-1, 0, 0, 1, 1])
_generate_circuit_library_visualization(circuit)
"""
def __init__(
self,
num_variable_qubits: int,
flags: list[int] | None = None,
mcx_mode: str = "noancilla",
) -> None:
"""Create a new logical AND circuit.
Args:
num_variable_qubits: The qubits of which the OR is computed. The result will be written
into an additional result qubit.
flags: A list of +1/0/-1 marking negations or omissions of qubits.
mcx_mode: The mode to be used to implement the multi-controlled X gate.
"""
self.num_variable_qubits = num_variable_qubits
self.flags = flags
# add registers
qr_variable = QuantumRegister(num_variable_qubits, name="variable")
qr_result = QuantumRegister(1, name="result")
circuit = QuantumCircuit(qr_variable, qr_result, name="and")
# determine the control qubits: all that have a nonzero flag
flags = flags or [1] * num_variable_qubits
control_qubits = [q for q, flag in zip(qr_variable, flags) if flag != 0]
# determine the qubits that need to be flipped (if a flag is < 0)
flip_qubits = [q for q, flag in zip(qr_variable, flags) if flag < 0]
# determine the number of ancillas
num_ancillas = MCXGate.get_num_ancilla_qubits(len(control_qubits), mode=mcx_mode)
if num_ancillas > 0:
qr_ancilla = AncillaRegister(num_ancillas, "ancilla")
circuit.add_register(qr_ancilla)
else:
qr_ancilla = AncillaRegister(0)
if len(flip_qubits) > 0:
circuit.x(flip_qubits)
circuit.mcx(control_qubits, qr_result[:], qr_ancilla[:], mode=mcx_mode)
if len(flip_qubits) > 0:
circuit.x(flip_qubits)
super().__init__(*circuit.qregs, name="and")
self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)