gdZddlmZddlZddlmZddlmZddlm Z ddl m Z m Z Gd d eZ d eed eed efdZdS)zFourier checking circuit.)SequenceN)QuantumCircuit) CircuitError)deprecate_func)Diagonal DiagonalGatecpeZdZdZeddddeedeedd ffd ZxZS) FourierCheckinga>Fourier checking circuit. The circuit for the Fourier checking algorithm, introduced in [1], involves a layer of Hadamards, the function :math:`f`, another layer of Hadamards, the function :math:`g`, followed by a final layer of Hadamards. The functions :math:`f` and :math:`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 :math:`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 :math:`p(f,g) <= 0.01` or :math:`p(f,g) >= 0.05`, promised that one or the other of these is true. The functions :math:`f` and :math:`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 :math:`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 `_ z1.3z4Use qiskit.circuit.library.fourier_checking instead.T)sinceadditional_msgpendingfgreturnNctjt|}t|t|ks|dks|st dt t |d|d|}||j| t|d||j| t|d||jtj |j d|ji| ||jd d S) aCreate Fourier checking circuit. Args: f: truth table for f, length 2**n list of {1,-1}. g: truth table for g, length 2**n list of {1,-1}. Raises: CircuitError: if the inputs f and g are not valid. Reference Circuit: .. plot:: :alt: Diagram illustrating the previously described circuit. from qiskit.circuit.library import FourierChecking from qiskit.visualization.library import _generate_circuit_library_visualization f = [1, -1, -1, -1] g = [1, 1, -1, -1] circuit = FourierChecking(f, g) _generate_circuit_library_visualization(circuit) r_The functions f and g must be given as truth tables, each as a list of 2**n entries of {1, -1}.fc: , nameT)inplacer)qubitsrN)mathlog2len is_integerrrinthrcomposersuper__init__qregsrto_gate)selfrr num_qubitscircuit __class__s ]/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/fourier_checking.pyr"zFourierChecking.__init__8sD4Ys1vv&& q66SVV  zQj6K6K6M6M !Za1GGG '.!!! T222 '.!!! T222 '.!!!'-;gl;;; W__&&t{D IIIII) __name__ __module__ __qualname____doc__rrrr" __classcell__)r(s@r)r r s<^M (J(3-(JHSM(Jd(J(J(J(J(J  (J(J(J(J(Jr*r rrrctjt|}t|t|ks|dks|st dt |}t |d|d|}||j| t|t|||j| t|t|||j|S)aUFourier checking circuit. The circuit for the Fourier checking algorithm, introduced in [1], involves a layer of Hadamards, the function :math:`f`, another layer of Hadamards, the function :math:`g`, followed by a final layer of Hadamards. The functions :math:`f` and :math:`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 :math:`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 :math:`p(f,g) <= 0.01` or :math:`p(f,g) >= 0.05`, promised that one or the other of these is true. The functions :math:`f` and :math:`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 :math:`k`-fold forrelation [2]. **Reference Circuit:** .. plot:: :alt: Circuit diagram output by the previous code. :include-source: 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 `_ rrrrr) rrrrrrrrrappendr range)rrr&r's r)fourier_checkingr3hsP3q66""J 1vvQ:??*2G2G2I2I?    ZJZoQoo!oo>>>G IIgn NN<??E*$5$5666 IIgn NN<??E*$5$5666 IIgn Nr*)r.collections.abcrrqiskit.circuitrqiskit.circuit.exceptionsrqiskit.utils.deprecationrgeneralized_gates.diagonalrr r rr3r*r)r:s $$$$$$ ))))))222222333333>>>>>>>>LJLJLJLJLJnLJLJLJ^8 8(3-8N888888r*