# FourierChecking¶

class FourierChecking(f, g)[source]

Bases : 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 all-zeros 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.

Paramètres
• 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}.

Lève

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.

Type renvoyé

List[AncillaQubit]

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form

{“gate_name”: {(qubits, params): schedule}}

Type renvoyé

dict

clbits

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

Type renvoyé

List[Clbit]

data

Return the circuit data (instructions and context).

Renvoie

a list-like object containing the CircuitInstructions for each instruction.

Type renvoyé

QuantumCircuitData

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

Return the global phase of the circuit in radians.

Type renvoyé

Union[ParameterExpression, float]

instances = 87

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.

Type renvoyé

dict

num_ancillas

Return the number of ancilla qubits.

Type renvoyé

int

num_clbits

Return number of classical bits.

Type renvoyé

int

num_parameters

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

Type renvoyé

int

num_qubits

Return number of qubits.

Type renvoyé

int

op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

Type renvoyé

List[int]

Renvoie

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

Lève

AttributeError – When circuit is not scheduled.

parameters

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

Type renvoyé

ParameterView

prefix = 'circuit'
qubits

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

Type renvoyé

List[Qubit]