FourierChecking¶

class
FourierChecking
(f, g)[source]¶ Bases:
qiskit.circuit.quantumcircuit.QuantumCircuit
Fourier checking circuit.
The circuit for the Fourier checking algorithm, introduced in [1], involves a layer of Hadamards, the function \(f\), another layer of Hadamards, the function \(g\), followed by a final layer of Hadamards. The functions \(f\) and \(g\) are classical functions realized as phase oracles (diagonal operators with {1, 1} on the diagonal).
The probability of observing the allzeros string is \(p(f,g)\). The algorithm solves the promise Fourier checking problem, which decides if f is correlated with the Fourier transform of g, by testing if \(p(f,g) <= 0.01\) or \(p(f,g) >= 0.05\), promised that one or the other of these is true.
The functions \(f\) and \(g\) are currently implemented from their truth tables but could be represented concisely and implemented efficiently for special classes of functions.
Fourier checking is a special case of \(k\)fold forrelation [2].
Reference:
[1] S. Aaronson, BQP and the Polynomial Hierarchy, 2009 (Section 3.2). arXiv:0910.4698
[2] S. Aaronson, A. Ambainis, Forrelation: a problem that optimally separates quantum from classical computing, 2014. arXiv:1411.5729
Create Fourier checking circuit.
 Parameters
f (
List
[int
]) – truth table for f, length 2**n list of {1,1}.g (
List
[int
]) – truth table for g, length 2**n list of {1,1}.
 Raises
CircuitError – if the inputs f and g are not valid.
 Reference Circuit:
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.