# Source code for 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
# 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.
"""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 <https://arxiv.org/abs/0910.4698>`_
[2] S. Aaronson, A. Ambainis, Forrelation: a problem that
optimally separates quantum from classical computing, 2014.
`arXiv:1411.5729 <https://arxiv.org/abs/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:
.. jupyter-execute::
:hide-code:
from qiskit.circuit.library import FourierChecking
import qiskit.tools.jupyter
f = [1, -1, -1, -1]
g = [1, 1, -1, -1]
circuit = FourierChecking(f, g)
%circuit_library_info 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, name=circuit.name)
self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)
```