def test_fidelity():
#test with kets
up = JzKet(S(1)/2, S(1)/2)
down = JzKet(S(1)/2, -S(1)/2)
updown = (S(1)/sqrt(2))*up + (S(1)/sqrt(2))*down
#check with matrices
up_dm = represent(up * Dagger(up))
down_dm = represent(down * Dagger(down))
updown_dm = represent(updown * Dagger(updown))
assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
assert fidelity(up_dm, down_dm) < 1e-3
assert abs(fidelity(up_dm, updown_dm) - (S(1)/sqrt(2))) < 1e-3
assert abs(fidelity(updown_dm, down_dm) - (S(1)/sqrt(2))) < 1e-3
#check with density
up_dm = Density([up, 1.0])
down_dm = Density([down, 1.0])
updown_dm = Density([updown, 1.0])
assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
assert abs(fidelity(up_dm, down_dm)) < 1e-3
assert abs(fidelity(up_dm, updown_dm) - (S(1)/sqrt(2))) < 1e-3
assert abs(fidelity(updown_dm, down_dm) - (S(1)/sqrt(2))) < 1e-3
#check mixed states with density
updown2 = (sqrt(3)/2)*up + (S(1)/2)*down
d1 = Density([updown, 0.25], [updown2, 0.75])
d2 = Density([updown, 0.75], [updown2, 0.25])
assert abs(fidelity(d1, d2) - 0.991) < 1e-3
assert abs(fidelity(d2, d1) - fidelity(d1, d2)) < 1e-3
#using qubits/density(pure states)
state1 = Qubit('0')
state2 = Qubit('1')
state3 = (S(1)/sqrt(2))*state1 + (S(1)/sqrt(2))*state2
state4 = (sqrt(S(2)/3))*state1 + (S(1)/sqrt(3))*state2
state1_dm = Density([state1, 1])
state2_dm = Density([state2, 1])
state3_dm = Density([state3, 1])
assert fidelity(state1_dm, state1_dm) == 1
assert fidelity(state1_dm, state2_dm) == 0
assert abs(fidelity(state1_dm, state3_dm) - 1/sqrt(2)) < 1e-3
assert abs(fidelity(state3_dm, state2_dm) - 1/sqrt(2)) < 1e-3
#using qubits/density(mixed states)
d1 = Density([state3, 0.70], [state4, 0.30])
d2 = Density([state3, 0.20], [state4, 0.80])
assert abs(fidelity(d1, d1) - 1) < 1e-3
assert abs(fidelity(d1, d2) - 0.996) < 1e-3
assert abs(fidelity(d1, d2) - fidelity(d2, d1)) < 1e-3
#TODO: test for invalid arguments
# non-square matrix
mat1 = [[0, 0],
[0, 0],
[0, 0]]
mat2 = [[0, 0],
[0, 0]]
raises(ValueError, lambda: fidelity(mat1, mat2))
# unequal dimensions
mat1 = [[0, 0],
[0, 0]]
mat2 = [[0, 0, 0],
[0, 0, 0],
[0, 0, 0]]
raises(ValueError, lambda: fidelity(mat1, mat2))
# unsupported data-type
x, y = 1, 2 # random values that is not a matrix
raises(ValueError, lambda: fidelity(x, y))
def test_fidelity():
#test with kets
up = JzKet(S(1) / 2, S(1) / 2)
down = JzKet(S(1) / 2, -S(1) / 2)
updown = (S(1) / sqrt(2)) * up + (S(1) / sqrt(2)) * down
#check with matrices
up_dm = represent(up * Dagger(up))
down_dm = represent(down * Dagger(down))
updown_dm = represent(updown * Dagger(updown))
assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
assert fidelity(up_dm, down_dm) < 1e-3
assert abs(fidelity(up_dm, updown_dm) - (S(1) / sqrt(2))) < 1e-3
assert abs(fidelity(updown_dm, down_dm) - (S(1) / sqrt(2))) < 1e-3
#check with density
up_dm = Density([up, 1.0])
down_dm = Density([down, 1.0])
updown_dm = Density([updown, 1.0])
assert abs(fidelity(up_dm, up_dm) - 1) < 1e-3
assert abs(fidelity(up_dm, down_dm)) < 1e-3
assert abs(fidelity(up_dm, updown_dm) - (S(1) / sqrt(2))) < 1e-3
assert abs(fidelity(updown_dm, down_dm) - (S(1) / sqrt(2))) < 1e-3
#check mixed states with density
updown2 = (sqrt(3) / 2) * up + (S(1) / 2) * down
d1 = Density([updown, 0.25], [updown2, 0.75])
d2 = Density([updown, 0.75], [updown2, 0.25])
assert abs(fidelity(d1, d2) - 0.991) < 1e-3
assert abs(fidelity(d2, d1) - fidelity(d1, d2)) < 1e-3
#using qubits/density(pure states)
state1 = Qubit('0')
state2 = Qubit('1')
state3 = (S(1) / sqrt(2)) * state1 + (S(1) / sqrt(2)) * state2
state4 = (sqrt(S(2) / 3)) * state1 + (S(1) / sqrt(3)) * state2
state1_dm = Density([state1, 1])
state2_dm = Density([state2, 1])
state3_dm = Density([state3, 1])
assert fidelity(state1_dm, state1_dm) == 1
assert fidelity(state1_dm, state2_dm) == 0
assert abs(fidelity(state1_dm, state3_dm) - 1 / sqrt(2)) < 1e-3
assert abs(fidelity(state3_dm, state2_dm) - 1 / sqrt(2)) < 1e-3
#using qubits/density(mixed states)
d1 = Density([state3, 0.70], [state4, 0.30])
d2 = Density([state3, 0.20], [state4, 0.80])
assert abs(fidelity(d1, d1) - 1) < 1e-3
assert abs(fidelity(d1, d2) - 0.996) < 1e-3
assert abs(fidelity(d1, d2) - fidelity(d2, d1)) < 1e-3
#TODO: test for invalid arguments
# non-square matrix
mat1 = [[0, 0], [0, 0], [0, 0]]
mat2 = [[0, 0], [0, 0]]
raises(ValueError, lambda: fidelity(mat1, mat2))
# unequal dimensions
mat1 = [[0, 0], [0, 0]]
mat2 = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
raises(ValueError, lambda: fidelity(mat1, mat2))
# unsupported data-type
x, y = 1, 2 # random values that is not a matrix
raises(ValueError, lambda: fidelity(x, y))