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fourier_checking
class qiskit.circuit.library.fourier_checking(f, g)
Bases:
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 Circuit:
from qiskit.circuit.library import fourier_checking
circuit = fourier_checking([1, -1, -1, -1], [1, 1, -1, -1])
circuit.draw('mpl')

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
Parameters
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