def test_to_numpy_matrix():
# Only numbers
phi = (1 / np.sqrt(2)) * (BaseQubitState("00").to_state() +
BaseQubitState("11").to_state())
op = outer_product(phi, phi)
expected = np.array([[1, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0],
[1, 0, 0, 1]]) / 2
print(op)
print(op.to_numpy_matrix())
assert np.all(np.isclose(op.to_numpy_matrix(), expected))
# Symbolic scalars
xy = InnerProductFunction("x", "y")
phi = xy * (BaseQubitState("00").to_state() +
BaseQubitState("11").to_state())
op = outer_product(phi, phi)
expected = np.array([[1, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0],
[1, 0, 0, 1]]) / 2
def convert_scalars(scalar):
return 1 / 2
print(op)
with pytest.raises(ValueError):
op.to_numpy_matrix()
m = op.to_numpy_matrix(convert_scalars=convert_scalars)
print(m)
assert np.all(np.isclose(m, expected))
def test_operator_dagger():
# Y (hermitian)
s0 = BaseQubitState("0").to_state()
s1 = BaseQubitState("1").to_state()
Y = outer_product(s1, s0) * 1j + outer_product(s0, s1) * (-1j)
print(Y)
assert Y == Y.dagger()
# T (non-hermitian)
s0 = BaseQubitState("0").to_state()
s1 = BaseQubitState("1").to_state()
T = outer_product(s0, s0) + outer_product(s1, s1) * np.exp(np.pi * 1j / 4)
print(T)
assert T != T.dagger()
def test_to_operator():
bs0 = BaseQubitState("0")
s0 = bs0.to_state()
bop0 = BaseOperator(bs0, bs0)
print(bop0.to_operator())
print(Operator([bop0]))
assert bop0.to_operator() == Operator([bop0])
assert bop0.to_operator() == outer_product(s0, s0)
def test_mul_state():
z0 = BaseQubitState("0").to_state()
z1 = BaseQubitState("1").to_state()
x0 = (z0 + z1) * (1 / np.sqrt(2))
x1 = (z0 - z1) * (1 / np.sqrt(2))
H = outer_product(x0, z0) + outer_product(x1, z1)
# Check the inner product after applying H
assert np.isclose((H * z0).inner_product(z0), 1 / np.sqrt(2))
assert np.isclose((H * z0).inner_product(z1), 1 / np.sqrt(2))
assert np.isclose((H * z0).inner_product(x0), 1)
assert np.isclose((H * z0).inner_product(x1), 0)
assert np.isclose((H * x0).inner_product(z0), 1)
assert np.isclose((H * x0).inner_product(z1), 0)
assert np.isclose((H * x0).inner_product(x0), 1 / np.sqrt(2))
assert np.isclose((H * x0).inner_product(x1), 1 / np.sqrt(2))
def construct_projector(num_left, num_right):
"""Construct the projector (eq. (46)-(51) in https://arxiv.org/abs/1903.09778)"""
vac = BaseFockState([]).to_state()
c1 = BaseFockState([FockOp('c', 'p1')]).to_state()
c2 = BaseFockState([FockOp('c', 'p2')]).to_state()
d1 = BaseFockState([FockOp('d', 'p1')]).to_state()
d2 = BaseFockState([FockOp('d', 'p2')]).to_state()
if (num_left, num_right) == (0, 0):
# P00
return outer_product(vac, vac)
elif (num_left, num_right) == (1, 0):
# P10
return outer_product(c1, c1)
elif (num_left, num_right) == (0, 1):
# P01
return outer_product(d1, d1)
elif (num_left, num_right) == (1, 1):
# P11
return outer_product(c1 @ d2, c1 @ d2)
elif (num_left, num_right) == (2, 0):
# P20
return outer_product(c1 @ c2, c1 @ c2)
elif (num_left, num_right) == (0, 2):
# P02
return outer_product(d1 @ d2, d1 @ d2)
else:
raise NotImplementedError()
def test_measurement():
s0 = BaseQubitState("0").to_state()
s1 = BaseQubitState("1").to_state()
h0 = (s0 + s1) * (1 / np.sqrt(2))
P0 = outer_product(s0, s0)
P1 = outer_product(s1, s1)
kraus_ops = {0: P0, 1: P1}
# Measure |0>
meas_res = measure(s0, kraus_ops)
assert meas_res.outcome == 0
assert np.isclose(meas_res.probability, 1)
# Measure |1>
meas_res = measure(s1, kraus_ops)
assert meas_res.outcome == 1
assert np.isclose(meas_res.probability, 1)
# Measure |+>
meas_res = measure(h0, kraus_ops)
assert np.isclose(meas_res.probability, 1 / 2)
def construct_beam_splitter():
"""Construct the beam splitter operation (eq. (40)-(41) in https://arxiv.org/abs/1903.09778)"""
fock_states = list(get_fock_states())
for i, state in enumerate(fock_states):
for old, new in zip(['w1', 'w2'], ['b1', 'b2']):
state = replace_var(state, old, new)
fock_states[i] = state
qubit_states = [
BaseQubitState(b).to_state() for b in ["00", "01", "10", "11"]
]
beam_splitter = sum(
(outer_product(fock_state, qubit_state)
for fock_state, qubit_state in zip(fock_states, qubit_states)),
Operator())
return beam_splitter.simplify()
def test_non_complete_kraus():
s0 = BaseQubitState("0").to_state()
s1 = BaseQubitState("1").to_state()
op = outer_product(s0, s0)
with pytest.raises(ValueError):
measure(s1, {"0": op})
def test_mul_operator_state():
s0 = BaseQubitState("0").to_state()
s1 = BaseQubitState("1").to_state()
splus = (s0 + s1) * (1 / np.sqrt(2))
op0 = outer_product(s0, s0)
assert s0 * (1 / np.sqrt(2)) == op0 * splus
def test_mul_operator_operator():
s0 = BaseQubitState("0").to_state()
op0 = outer_product(s0, s0)
assert op0 == op0 * op0