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
CircuitInstruction
s 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
]
- header = 'OPENQASM 2.0;'¶
- instances = 87¶
- 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.- 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'¶