FourierChecking
class FourierChecking(f, g)
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 , another layer of Hadamards, the function , followed by a final layer of Hadamards. The functions and are classical functions realized as phase oracles (diagonal operators with {-1, 1} on the diagonal).
The probability of observing the all-zeros string is . The algorithm solves the promise Fourier checking problem, which decides if f is correlated with the Fourier transform of g, by testing if or , promised that one or the other of these is true.
The functions and 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 -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.
Return type
List[AncillaQubit]
calibrations
Return calibration dictionary.
The custom pulse definition of a given gate is of the form
{‘gate_name’: {(qubits, params): schedule}}
Return type
dict
clbits
Returns a list of classical bits in the order that the registers were added.
Return type
List[Clbit]
data
Return the circuit data (instructions and context).
Returns
a list-like 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
Default value: 'include "qelib1.inc";'
global_phase
Return the global phase of the circuit in radians.
Return type
Union[ParameterExpression, float]
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 9
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.
Return type
dict
num_ancillas
Return the number of ancilla qubits.
Return type
int
num_clbits
Return number of classical bits.
Return type
int
num_parameters
Convenience function to get the number of parameter objects in the circuit.
Return type
int
num_qubits
Return number of qubits.
Return type
int
parameters
Convenience function to get the parameters defined in the parameter table.
Return type
ParameterView
prefix
Default value: 'circuit'
qubits
Returns a list of quantum bits in the order that the registers were added.
Return type
List[Qubit]