Code source de qiskit.circuit.library.fourier_checking

# 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
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"""Fourier checking circuit."""

from typing import List

import math
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.exceptions import CircuitError

[docs]class FourierChecking(QuantumCircuit): """Fourier checking circuit. The circuit for the Fourier checking algorithm, introduced in [1], involves a layer of Hadamards, the function :math:`f`, another layer of Hadamards, the function :math:`g`, followed by a final layer of Hadamards. The functions :math:`f` and :math:`g` are classical functions realized as phase oracles (diagonal operators with {-1, 1} on the diagonal). The probability of observing the all-zeros string is :math:`p(f,g)`. The algorithm solves the promise Fourier checking problem, which decides if f is correlated with the Fourier transform of g, by testing if :math:`p(f,g) <= 0.01` or :math:`p(f,g) >= 0.05`, promised that one or the other of these is true. The functions :math:`f` and :math:`g` are currently implemented from their truth tables but could be represented concisely and implemented efficiently for special classes of functions. Fourier checking is a special case of :math:`k`-fold forrelation [2]. **Reference:** [1] S. Aaronson, BQP and the Polynomial Hierarchy, 2009 (Section 3.2). `arXiv:0910.4698 <>`_ [2] S. Aaronson, A. Ambainis, Forrelation: a problem that optimally separates quantum from classical computing, 2014. `arXiv:1411.5729 <>`_ """ def __init__(self, f: List[int], g: List[int]) -> None: """Create Fourier checking circuit. Args: f: truth table for f, length 2**n list of {1,-1}. g: truth table for g, length 2**n list of {1,-1}. Raises: CircuitError: if the inputs f and g are not valid. Reference Circuit: .. plot:: from qiskit.circuit.library import FourierChecking from import _generate_circuit_library_visualization f = [1, -1, -1, -1] g = [1, 1, -1, -1] circuit = FourierChecking(f, g) _generate_circuit_library_visualization(circuit) """ num_qubits = math.log2(len(f)) if len(f) != len(g) or num_qubits == 0 or not num_qubits.is_integer(): raise CircuitError( "The functions f and g must be given as truth " "tables, each as a list of 2**n entries of " "{1, -1}." ) circuit = QuantumCircuit(num_qubits, name=f"fc: {f}, {g}") circuit.h(circuit.qubits) circuit.diagonal(f, circuit.qubits) circuit.h(circuit.qubits) circuit.diagonal(g, circuit.qubits) circuit.h(circuit.qubits) super().__init__(*circuit.qregs, self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)