%autosave 0
from sglib import *
from sympy.physics.quantum.qubit import matrix_to_qubit

I = mat(1,0,0,1)
NOT = X = sigma_x
H = mat(1,1,1,-1)/sqrt(2)
Print('$I = %s$' %myltx(I))
Print('$X = %s$' %myltx(X))
Print('$H = %s$' %myltx(H))

H = 1/sqrt(2)*Matrix([(1,1),(1,-1)])
SN1 = 1/sqrt(2)*Matrix([(i,1),(1,i)])
SN2 = 1/sqrt(2)*Matrix([(1,i),(i,1)])
sg_print(H)
sg_print(SN1)
sg_print(SN2)
H*H, SN1*SN1, SN2*SN2, SN1*SN1*col(1,0)

SWAP = mat(1,0,0,0, 0,0,1,0, 0,1,0,0, 0,0,0,1)
SWAP

a_1 = sy.Symbol('a_1'); a_2 = sy.Symbol('a_2');
b_1 = sy.Symbol('b_1'); b_2 = sy.Symbol('b_2')
a = col(a_1, a_2); b = col(b_1, b_2)
# NOTE: "TP" is the Tensor Product
state = TP(a,b)
Print('Before: $%s$'%latex(state))
Print('After : $%s$'%latex(SWAP*state))

zero = col(1,0); one = col(0,1)
state = TP(zero, one)
Print('SWAP $%s = %s$'
      %(latex(matrix_to_qubit(state)), latex(matrix_to_qubit(SWAP*state))))
state = TP(one, zero)
Print('SWAP $%s = %s$'
      %(latex(matrix_to_qubit(state)), latex(matrix_to_qubit(SWAP*state))))

CNOT = mat(1,0,0,0, 0,1,0,0, 0,0,0,1, 0,0,1,0)
CNOT

state = TP(zero, zero)
Print('CNOT $%s = %s$'
      %(latex(matrix_to_qubit(state)), latex(matrix_to_qubit(CNOT*state))))
state = TP(zero, one)
Print('CNOT $%s = %s$'
      %(latex(matrix_to_qubit(state)), latex(matrix_to_qubit(CNOT*state))))
state = TP(one, zero)
Print('CNOT $%s = %s$'
      %(latex(matrix_to_qubit(state)), latex(matrix_to_qubit(CNOT*state))))
state = TP(one, one)
Print('CNOT $%s = %s$'
      %(latex(matrix_to_qubit(state)), latex(matrix_to_qubit(CNOT*state))))