HiddenLinearFunction¶

class
HiddenLinearFunction
(adjacency_matrix)[source]¶ Bases:
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 nearestneighbor on a grid have nonzero 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 \([z_0, ..., z_{n1}]\)). 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.
 Parameters
adjacency_matrix (
Union
[List
[List
[int
]],ndarray
]) – a symmetric nbyn list of 01 lists. n will be the number of qubits. Raises
CircuitError – If A is not symmetric.
Attributes

ancillas
¶ Returns a list of ancilla bits in the order that the registers were added.

calibrations
¶ Return calibration dictionary.
 The custom pulse definition of a given gate is of the form
{‘gate_name’: {(qubits, params): schedule}}

clbits
¶ Returns a list of classical bits in the order that the registers were added.

data
¶ Return the circuit data (instructions and context).
 Returns
a listlike object containing the tuples for the circuit’s data.
Each tuple is in the format
(instruction, qargs, cargs)
, where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects. Return type
QuantumCircuitData

extension_lib
= 'include "qelib1.inc";'¶

global_phase
¶ Return the global phase of the circuit in radians.

header
= 'OPENQASM 2.0;'¶

instances
= 16¶

metadata
¶ The user provided metadata associated with the circuit
The metadata for the circuit is a user provided
dict
of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

num_ancillas
¶ Return the number of ancilla qubits.

num_clbits
¶ Return number of classical bits.

num_parameters
¶ Convenience function to get the number of parameter objects in the circuit.

num_qubits
¶ Return number of qubits.

parameters
¶ Convenience function to get the parameters defined in the parameter table.

prefix
= 'circuit'¶

qubits
¶ Returns a list of quantum bits in the order that the registers were added.