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
data
Return the circuit data (instructions and context).
Returns
a list-like object containing the CircuitInstructions for each instruction.
Return type
QuantumCircuitData
extension_lib
Default value: 'include "qelib1.inc";'
global_phase
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 2310
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
The number of parameter objects in the circuit.
Return type
int
num_qubits
Return number of qubits.
Return type
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.
Return type
List[int]
Returns
List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.
Raises
AttributeError – When circuit is not scheduled.
parameters
The parameters defined in the circuit.
This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.
Examples
The snippet below shows that insertion order of parameters does not matter.
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])Bear in mind that alphabetical sorting might be unituitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
└─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])To respect numerical sorting, a ParameterVector can be used.
>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
... circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
..., ParameterVectorElement(x[11])
])Return type
ParameterView
Returns
The sorted Parameter objects in the circuit.
prefix
Default value: 'circuit'