qiskit.circuit.library.hidden_linear_function

qiskit.circuit.library.hidden_linear_function(adjacency_matrix)

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

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

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:

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')

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.

Return type

QuantumCircuit

Reference:

[1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. arXiv:1704.00690