def __init__(self):
try:
lazy_import()
except ImportError:
raise ImportError('sympy_unitary requires sympy. Please install before call this option.')
theta, phi, lambd = symbols('theta phi lambd')
self.theta = theta
self.phi = phi
self.lambd = lambd
self.SYMPY_GATE = {
'X': sympy_gate.X(0).get_target_matrix(),
'Y': sympy_gate.Y(0).get_target_matrix(),
'Z': sympy_gate.Z(0).get_target_matrix(),
'H': sympy_gate.H(0).get_target_matrix(),
'T': sympy_gate.T(0).get_target_matrix(),
'S': sympy_gate.S(0).get_target_matrix(),
'RX': Matrix([[cos(theta / 2), -I * sin(theta / 2)], [-I * sin(theta / 2), cos(theta / 2)]]),
'RY': Matrix([[cos(theta / 2), -sin(theta / 2)], [sin(theta / 2), cos(theta / 2)]]),
'RZ': Matrix([[exp(-I * theta / 2), 0], [0, exp(I * theta / 2)]]),
'TARGET_CX': sympy_gate.X(0).get_target_matrix(),
'TARGET_CZ': sympy_gate.Z(0).get_target_matrix(),
'U1': Matrix([[exp(-I * lambd / 2), 0], [0, exp(I * lambd / 2)]]),
'U2': Matrix([
[exp(-I * (phi + lambd) / 2) / sqrt(2), -exp(-I * (phi - lambd) / 2) / sqrt(2)],
[exp(I * (phi - lambd) / 2) / sqrt(2), exp(I * (phi + lambd) / 2) / sqrt(2)]]),
'U3': Matrix([
[exp(-I * (phi + lambd) / 2) * cos(theta / 2), -exp(-I * (phi - lambd) / 2) * sin(theta / 2)],
[exp(I * (phi - lambd) / 2) * sin(theta / 2), exp(I * (phi + lambd) / 2) * cos(theta / 2)]]),
}
def test_sympy_backend_for_one_qubit_gate():
E = eye(2)
X = gate.X(0).get_target_matrix()
Y = gate.Y(0).get_target_matrix()
Z = gate.Z(0).get_target_matrix()
H = gate.H(0).get_target_matrix()
T = gate.T(0).get_target_matrix()
S = gate.S(0).get_target_matrix()
x, y, z = symbols('x, y, z')
RX = Matrix([[cos(x / 2), -I * sin(x / 2)], [-I * sin(x / 2), cos(x / 2)]])
RY = Matrix([[cos(y / 2), -sin(y / 2)], [sin(y / 2), cos(y / 2)]])
RZ = Matrix([[exp(-I * z / 2), 0], [0, exp(I * z / 2)]])
actual_1 = Circuit().x[0, 1].y[1].z[2].run(backend="sympy_unitary")
expected_1 = reduce(TensorProduct, [Z, Y * X, X])
assert actual_1 == expected_1
actual_2 = Circuit().y[0].z[3].run(backend="sympy_unitary")
expected_2 = reduce(TensorProduct, [Z, E, E, Y])
assert actual_2 == expected_2
actual_3 = Circuit().x[0].z[3].h[:].t[1].s[2].run(backend="sympy_unitary")
expected_3 = reduce(TensorProduct, [H * Z, S * H, T * H, H * X])
assert actual_3 == expected_3
actual_4 = Circuit().rx(-pi / 2)[0].rz(
pi / 2)[1].ry(pi)[2].run(backend="sympy_unitary")
expected_4 = reduce(TensorProduct, [RY, RZ, RX]).subs([[x,
-pi / 2], [y, pi],
[z, pi / 2]])
assert actual_4 == expected_4
def test_sympy_backend_for_two_qubit_gate():
E = eye(2)
UPPER = Matrix([[1, 0], [0, 0]])
LOWER = Matrix([[0, 0], [0, 1]])
X = gate.X(0).get_target_matrix()
Z = gate.Z(0).get_target_matrix()
H = gate.H(0).get_target_matrix()
H_3 = reduce(TensorProduct, [H, E, H])
H_4 = reduce(TensorProduct, [H, E, E, H])
CX_3 = reduce(TensorProduct, [E, E, UPPER]) + reduce(
TensorProduct, [X, E, LOWER])
CZ_3 = reduce(TensorProduct, [E, E, UPPER]) + reduce(
TensorProduct, [Z, E, LOWER])
CX_4 = reduce(TensorProduct, [E, E, E, UPPER]) + reduce(
TensorProduct, [X, E, E, LOWER])
CZ_4 = reduce(TensorProduct, [E, E, E, UPPER]) + reduce(
TensorProduct, [Z, E, E, LOWER])
actual_1 = Circuit().cx[0, 3].run(backend="sympy_unitary")
assert actual_1 == CX_4
actual_2 = Circuit().cx[1, 3].x[4].run(backend="sympy_unitary")
expected_2 = reduce(TensorProduct, [X, CX_3, E])
assert actual_2 == expected_2
actual_3 = Circuit().cz[0, 3].run(backend="sympy_unitary")
assert actual_3 == CZ_4
actual_4 = Circuit().cz[1, 3].x[4].run(backend="sympy_unitary")
expected_4 = reduce(TensorProduct, [X, CZ_3, E])
assert actual_4 == expected_4
actual_5 = Circuit().cx[3, 0].run(backend="sympy_unitary")
assert actual_5 == H_4 * CX_4 * H_4
actual_6 = Circuit().cx[3, 1].x[4].run(backend="sympy_unitary")
assert actual_6 == reduce(TensorProduct, [X, H_3 * CX_3 * H_3, E])
actual_7 = Circuit().cz[3, 0].run(backend="sympy_unitary")
assert actual_7 == CZ_4
actual_8 = Circuit().cz[3, 1].x[4].run(backend="sympy_unitary")
assert actual_8 == reduce(TensorProduct, [X, CZ_3, E])
def test_sympy_backend_for_two_qubit_gate():
E = eye(2)
UPPER = Matrix([[1, 0], [0, 0]])
LOWER = Matrix([[0, 0], [0, 1]])
X = gate.X(0).get_target_matrix()
Z = gate.Z(0).get_target_matrix()
H = gate.H(0).get_target_matrix()
H_3 = reduce(TensorProduct, [H, E, H])
H_4 = reduce(TensorProduct, [H, E, E, H])
CX_3 = reduce(TensorProduct, [E, E, UPPER]) + reduce(
TensorProduct, [X, E, LOWER])
CZ_3 = reduce(TensorProduct, [E, E, UPPER]) + reduce(
TensorProduct, [Z, E, LOWER])
CX_4 = reduce(TensorProduct, [E, E, E, UPPER]) + reduce(
TensorProduct, [X, E, E, LOWER])
CZ_4 = reduce(TensorProduct, [E, E, E, UPPER]) + reduce(
TensorProduct, [Z, E, E, LOWER])
actual_1 = Circuit().cx[0, 3].run(backend="sympy_unitary")
assert actual_1 == CX_4
actual_2 = Circuit().cx[1, 3].x[4].run(backend="sympy_unitary")
expected_2 = reduce(TensorProduct, [X, CX_3, E])
assert actual_2 == expected_2
actual_3 = Circuit().cz[0, 3].run(backend="sympy_unitary")
assert actual_3 == CZ_4
actual_4 = Circuit().cz[1, 3].x[4].run(backend="sympy_unitary")
expected_4 = reduce(TensorProduct, [X, CZ_3, E])
assert actual_4 == expected_4
actual_5 = Circuit().cx[3, 0].run(backend="sympy_unitary")
assert actual_5 == H_4 * CX_4 * H_4
actual_6 = Circuit().cx[3, 1].x[4].run(backend="sympy_unitary")
assert actual_6 == reduce(TensorProduct, [X, H_3 * CX_3 * H_3, E])
actual_7 = Circuit().cz[3, 0].run(backend="sympy_unitary")
assert actual_7 == CZ_4
actual_8 = Circuit().cz[3, 1].x[4].run(backend="sympy_unitary")
assert actual_8 == reduce(TensorProduct, [X, CZ_3, E])
x, y, z = symbols('x, y, z')
RX = Matrix([[cos(x / 2), -I * sin(x / 2)], [-I * sin(x / 2), cos(x / 2)]])
RY = Matrix([[cos(y / 2), -sin(y / 2)], [sin(y / 2), cos(y / 2)]])
RZ = Matrix([[exp(-I * z / 2), 0], [0, exp(I * z / 2)]])
CRX_3 = reduce(TensorProduct, [UPPER, E, E]) + reduce(
TensorProduct, [LOWER, E, RX])
CRY_4 = reduce(TensorProduct, [E, UPPER, E, E]) + reduce(
TensorProduct, [E, LOWER, RY, E])
CRZ_3 = reduce(TensorProduct, [E, E, UPPER]) + reduce(
TensorProduct, [RZ, E, LOWER])
actual_9 = Circuit().crx(x)[2, 0].run(backend="sympy_unitary")
assert simplify(actual_9) == CRX_3
actual_10 = Circuit().cry(y)[2, 1].i[3].run(backend="sympy_unitary")
assert simplify(actual_10) == CRY_4
actual_11 = Circuit().crz(z)[0, 2].run(backend="sympy_unitary")
assert simplify(actual_11) == CRZ_3