HiddenLinearFunction

class qiskit.circuit.library.HiddenLinearFunction(adjacency_matrix)

Bases: 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:

Reference:

[1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. arXiv: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 | np.ndarray) – a symmetric n-by-n list of 0-1 lists. n will be the number of qubits.

Raises

CircuitError – If A is not symmetric.

Attributes

name

Type: str

A human-readable name for the circuit.

Example

from qiskit import QuantumCircuit
 
qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)

my_circuit