---
title: fourier_checking (v1.3)
description: API reference for qiskit.circuit.library.fourier_checking in qiskit v1.3
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/1.3/qiskit.circuit.library.fourier_checking
---

# fourier\_checking

*class* `qiskit.circuit.library.fourier_checking(f, g)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/fourier_checking.py#L104-L160)

Bases:

Fourier checking circuit.

The circuit for the Fourier checking algorithm, introduced in \[1], involves a layer of Hadamards, the function $f$, another layer of Hadamards, the function $g$, followed by a final layer of Hadamards. The functions $f$ and $g$ are classical functions realized as phase oracles (diagonal operators with \{-1, 1} on the diagonal).

The probability of observing the all-zeros string is $p(f,g)$. The algorithm solves the promise Fourier checking problem, which decides if f is correlated with the Fourier transform of g, by testing if $p(f,g) <= 0.01$ or $p(f,g) >= 0.05$, promised that one or the other of these is true.

The functions $f$ and $g$ 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 $k$-fold forrelation \[2].

**Reference Circuit:**

```python
from qiskit.circuit.library import fourier_checking
circuit = fourier_checking([1, -1, -1, -1], [1, 1, -1, -1])
circuit.draw('mpl')
```

![Circuit diagram output by the previous code.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/1.3/qiskit-circuit-library-fourier_checking-1.avif)

**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)

**Parameters**

- **f** ([*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]*) –
- **g** ([*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]*) –

**Return type**

[*QuantumCircuit*](/docs/api/qiskit/1.3/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")