z iSrSSKJr SSKrSSKJr SSKJr SSKJ r SSK J r J r "S S \5r S \\S \\S \4Sjrg)zFourier checking circuit.)SequenceN)QuantumCircuit) CircuitError)deprecate_func)Diagonal DiagonalGatec^^\rSrSrSr\"SSSS9S\\S\\S S 4U4S jj5rS r U=r $) FourierCheckingaFourier 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]. References: [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 `_ z2.1z4Use qiskit.circuit.library.fourier_checking instead.z in Qiskit 3.0)sinceadditional_msgremoval_timelinefgreturnNc>[R"[U55n[U5[U5:wdUS:XdUR5(d [ S5e[ [ U5SUSU3S9nURUR5 UR[U5SS9 URUR5 UR[U5SS9 URUR5 [TU]0"URSUR06 URUR5URSS 9 g ) aaCreate 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 a/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/fourier_checking.pyr#FourierChecking.__init__8s4YYs1v& q6SV zQj6K6K6M6M !ZaS1#G '..! T2 '..! T2 '..! '--;gll; W__&t{{D I) __name__ __module__ __qualname____firstlineno____doc__rrrr#__static_attributes__ __classcell__)r)s@r*r r sL<M( (J(3-(JHSM(Jd(J  (Jr,r rrrc([R"[U55n[U5[U5:wdUS:XdUR5(d [ S5e[ U5n[ USUSU3S9nURUR5 UR[U5[U55 URUR5 UR[U5[U55 URUR5 U$)aFourier 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') References: [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) rrrrrrrr rappendr range)rrr'r(s r*fourier_checkingr8hsP3q6"J 1vQ:?*2G2G2I2I   ZJZQCr!o>G IIgnn NN<?E*$56 IIgnn NN<?E*$56 IIgnn Nr,)r2collections.abcrrqiskit.circuitrqiskit.circuit.exceptionsrqiskit.utils.deprecationrgeneralized_gates.diagonalrr r rr8r-r,r*r>sO $ )23>LJnLJ^8 8(3-8N8r,