Python/quantum/qauntum_logic_gates.py

"""
Quantum Logic Gates which are implemented mathematically
and can be used as functions to build complex calculations
and implement different operations. The input taken is a real value
and imaginary value of the number and the result is output after computation.

References :
https://en.wikipedia.org/wiki/Quantum_logic_gate

Book : Mathematics Of Quantum Computing An Introduction by Wolfgang Scherer

Glossary ;
input_realvalue : the magnitude of the real part of the input complex number.
input_imaginaryvalue : the magnitude of the imaginary part of the input complex number.
In cases which require 2 inputs the input is named with a suffix of 1 and 2
(Eg. input_realvalue_1)

alpha : angle of rotation as represented by the block sphere.
iota : The exponential complex of alpha value.
nx_value : value of vector in X axis as represented by Hilbert space.
nx_value : value of vector in Y axis as represented by Hilbert space.
nx_value : value of vector in Z axis as represented by Hilbert space.

* The nx,ny and nz values can also be considered as values of vectors along
the respective axes on the bloch sphere.

Usage :
>>> paulix_gate(2,3)
[3 2]

>>> pauliy_gate(5,8)
[0.+8.j 0.-5.j]

>>> pauliz_gate(4,1)
[ 4 -1]

>>> identity_gate(7,2)
9

>>> phasefactor_of_input(4,7,45)
[1.39737084e+20+0.j 2.44539897e+20+0.j]

>>> phaseshift_of_input(3,9,30)
[3.00000000e+00+0.j 9.61782712e+13+0.j]

>>> hadamard_gate(5,9)
[ 9.89949494 -2.82842712]
[1.+0.j 0.+0.j 0.+0.j 7.+0.j]

>>> controlled_not_gate_in_0ket(1,7,4,8)
[7 1 4 8]

>>> controlled_not_gate(6,3,7,5)
[6 3 5 7]

>>> inverted_controlled_not_gate(8,4,9,6)
[8 6 9 4]

>>> controlled_phase_multiplication(3,2,5,1,10)
[3.00000000e+00+0.j 2.00000000e+00+0.j 1.10132329e+05+0.j
 2.20264658e+04+0.j]

>>> swap_gate(5,1,3,7)
[5 3 1 7]

>>> spin_of_input(6,3,45,1,8,3)
[-16.93201614+10.23066476j -50.61991392 -1.46152354j]

"""

import cmath
import math

import numpy as np


def paulix_gate(input_realvalue, input_imaginaryvalue):
    paulix_matrix = np.array([[0, 1], [1, 0]])
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(paulix_matrix, complex_input)
    return result


def pauliy_gate(input_realvalue, input_imaginaryvalue):
    i = complex(0, 1)
    pauliy_matrix = [[0, i], [-1 * i, 0]]
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(pauliy_matrix, complex_input)
    return result


def pauliz_gate(input_realvalue, input_imaginaryvalue):
    pauliz_matrix = np.array([[1, 0], [0, -1]])
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(pauliz_matrix, complex_input)
    return result


def identity_gate(input_realvalue, input_imaginaryvalue):
    identiy_matrix = np.diag([[1, 0], [0, 1]])
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(identiy_matrix, complex_input)
    return result


def phasefactor_of_input(input_realvalue, input_imaginaryvalue, alpha):
    iota = cmath.exp(alpha)
    phasefactor = [[iota, 0], [0, iota]]
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(phasefactor, complex_input)
    return result


def phaseshift_of_input(input_realvalue, input_imaginaryvalue, alpha):
    iota = cmath.exp(alpha)
    phase = [[1, 0], [0, iota]]
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(phase, complex_input)
    return result


def hadamard_gate(input_realvalue, input_imaginaryvalue):
    root_of_2 = 1.0 / math.sqrt(2)
    hadamard_gate_matrix = np.array(
        [[root_of_2, root_of_2], [root_of_2, -1 * root_of_2]]
    )
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(hadamard_gate_matrix, complex_input)
    return result


def controlled_not_gate_in_0ket(
    input_realvalue_1, input_imaginaryvalue_1, input_realvalue_2, input_imaginaryvalue_2
):
    controlled_not_gate_0ket_matrix = np.array(
        [[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
    )
    complex_input = np.array(
        [
            input_realvalue_1,
            input_imaginaryvalue_1,
            input_realvalue_2,
            input_imaginaryvalue_2,
        ]
    )
    print(complex_input)
    result = np.dot(controlled_not_gate_0ket_matrix, complex_input)
    return result


def controlled_not_gate(
    input_realvalue_1, input_imaginaryvalue_1, input_realvalue_2, input_imaginaryvalue_2
):
    controlled_not_gate_matrix = np.array(
        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]
    )
    complex_input = np.array(
        [
            input_realvalue_1,
            input_imaginaryvalue_1,
            input_realvalue_2,
            input_imaginaryvalue_2,
        ]
    )
    result = np.dot(controlled_not_gate_matrix, complex_input)
    return result


def inverted_controlled_not_gate(
    input_realvalue_1, input_imaginaryvalue_1, input_realvalue_2, input_imaginaryvalue_2
):
    inverted_controlled_not_gate_matrix = np.array(
        [[1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]]
    )
    complex_input = np.array(
        [
            input_realvalue_1,
            input_imaginaryvalue_1,
            input_realvalue_2,
            input_imaginaryvalue_2,
        ]
    )
    result = np.dot(inverted_controlled_not_gate_matrix, complex_input)
    return result


def controlled_phase_multiplication(
    input_realvalue_1,
    input_imaginaryvalue_1,
    input_realvalue_2,
    input_imaginaryvalue_2,
    alpha,
):
    iota = cmath.exp(alpha)
    controlled_phase_multiplication_matrix = np.array(
        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, iota, 0], [0, 0, 0, iota]]
    )
    complex_input = np.array(
        [
            input_realvalue_1,
            input_imaginaryvalue_1,
            input_realvalue_2,
            input_imaginaryvalue_2,
        ]
    )
    result = np.dot(controlled_phase_multiplication_matrix, complex_input)
    return result


def swap_gate(
    input_realvalue_1, input_imaginaryvalue_1, input_realvalue_2, input_imaginaryvalue_2
):
    swap_gate_matrix = np.array(
        [[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]
    )
    complex_input = np.array(
        [
            input_realvalue_1,
            input_imaginaryvalue_1,
            input_realvalue_2,
            input_imaginaryvalue_2,
        ]
    )
    result = np.dot(swap_gate_matrix, complex_input)
    return result


def spin_of_input(
    input_realvalue, input_imaginaryvalue, alpha_value, nx_value, ny_value, nz_value
):
    i = complex(0, 1)
    spin_matrix = [
        [
            (math.cos(alpha_value / 2.0))
            - (i * math.sin(alpha_value / 2.0) * nz_value),
            (-1 * i * math.sin(alpha_value / 2.0) * (nx_value + i * ny_value)),
        ],
        [
            -1 * i * (math.sin(alpha_value / 2.0) * nx_value - i * ny_value),
            math.cos(alpha_value / 2.0) + (i * math.sin(alpha_value / 2.0) * nz_value),
        ],
    ]
    complex_input = np.array([input_realvalue, input_imaginaryvalue])
    result = np.dot(spin_matrix, complex_input)
    return result


if __name__ == "__main__":
    import doctest

    doctest.testmod()