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

# hidden\_linear\_function

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

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/hidden_linear_function.py#L92-L163)

Bases:

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:**

```python
from qiskit.circuit.library import hidden_linear_function
A = [[1, 1, 0], [1, 0, 1], [0, 1, 1]]
circuit = hidden_linear_function(A)
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-hidden_linear_function-1.avif)

**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/1.3/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If A is not symmetric.

**Return type**

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

**Reference:**

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