---
title: HiddenLinearFunction (v2.3)
description: API reference for qiskit.circuit.library.HiddenLinearFunction in qiskit v2.3
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.3/qiskit.circuit.library.HiddenLinearFunction
---

# HiddenLinearFunction

*class* `qiskit.circuit.library.HiddenLinearFunction(adjacency_matrix)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.3/qiskit/circuit/library/hidden_linear_function.py#L23-L89)

Bases: [`QuantumCircuit`](/docs/api/qiskit/2.3/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")

Circuit to solve the hidden linear function problem.

The 2D Hidden Linear Function problem is determined by a 2D adjacency matrix A, where only elements that are nearest-neighbor on a grid have non-zero entries. Each row/column corresponds to one binary variable $x_i$.

The hidden linear function problem is as follows:

Consider the quadratic form

$$
q(x) = \sum_{i,j=1}^{n}{x_i x_j} ~(\mathrm{mod}~ 4)
$$

and restrict $q(x)$ onto the nullspace of A. This results in a linear function.

$$
2 \sum_{i=1}^{n}{z_i x_i} ~(\mathrm{mod}~ 4)  \forall  x \in \mathrm{Ker}(A)
$$

and the goal is to recover this linear function (equivalently a vector $[z_0, ..., z_{n-1}]$). There can be multiple solutions.

In \[1] it is shown that the present circuit solves this problem on a quantum computer in constant depth, whereas any corresponding solution on a classical computer would require circuits that grow logarithmically with $n$. Thus this circuit is an example of quantum advantage with shallow circuits.

Reference Circuit:

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.3/qiskit-circuit-library-HiddenLinearFunction-1.avif)

References:

\[1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. [arXiv:1704.00690](https://arxiv.org/abs/1704.00690)

Create new HLF circuit.

> **Deprecated since version 2.1**
>
> The class `qiskit.circuit.library.hidden_linear_function.HiddenLinearFunction` is deprecated as of Qiskit 2.1. It will be removed in Qiskit 3.0. Use qiskit.circuit.library.hidden\_linear\_function instead.

**Parameters**

**adjacency\_matrix** ([*list*](https://docs.python.org/3/library/stdtypes.html#list) *| np.ndarray*) – a symmetric n-by-n list of 0-1 lists. n will be the number of qubits.

**Raises**

[**CircuitError**](/docs/api/qiskit/2.3/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If A is not symmetric.

## 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
```