---
title: FourierChecking (v2.1)
description: API reference for qiskit.circuit.library.FourierChecking in qiskit v2.1
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.1/qiskit.circuit.library.FourierChecking
---

# FourierChecking

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

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.1/qiskit/circuit/library/fourier_checking.py#L25-L101)

Bases: [`QuantumCircuit`](/docs/api/qiskit/2.1/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")

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:**

\[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)

Create Fourier checking circuit.

> **Deprecated since version 2.1**
>
> The class `qiskit.circuit.library.fourier_checking.FourierChecking` is deprecated as of Qiskit 2.1. It will be removed in Qiskit 3.0. Use qiskit.circuit.library.fourier\_checking instead.

**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)*]*) – truth table for f, length 2\*\*n list of \{1,-1}.
- **g** ([*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]*) – truth table for g, length 2\*\*n list of \{1,-1}.

**Raises**

[**CircuitError**](/docs/api/qiskit/2.1/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – if the inputs f and g are not valid.

**Reference Circuit:**

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.1/qiskit-circuit-library-FourierChecking-1.avif)

## Attributes

### name

Type: `str`

A human-readable name for the circuit.

**Example**

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)
```

```text
my_circuit
```