def test_fubini_study_angle():
for _ in range(REPS):
theta = random.uniform(-pi, +pi)
ang = qf.asarray(qf.fubini_study_angle(qf.I().vec, qf.RX(theta).vec))
assert 2 * ang / abs(theta) == ALMOST_ONE
ang = qf.asarray(qf.fubini_study_angle(qf.I().vec, qf.RY(theta).vec))
assert 2 * ang / abs(theta) == ALMOST_ONE
ang = qf.asarray(qf.fubini_study_angle(qf.I().vec, qf.RZ(theta).vec))
assert 2 * ang / abs(theta) == ALMOST_ONE
ang = qf.asarray(
qf.fubini_study_angle(qf.SWAP().vec,
qf.PSWAP(theta).vec))
assert 2 * ang / abs(theta) == ALMOST_ONE
ang = qf.asarray(qf.fubini_study_angle(qf.I().vec,
qf.PHASE(theta).vec))
assert 2 * ang / abs(theta) == ALMOST_ONE
for n in range(1, 6):
eye = qf.identity_gate(n)
assert qf.asarray(qf.fubini_study_angle(eye.vec, eye.vec)) \
== ALMOST_ZERO
with pytest.raises(ValueError):
qf.fubini_study_angle(qf.random_gate(1).vec, qf.random_gate(2).vec)
def test_fubini_study_angle() -> None:
for _ in range(REPS):
theta = random.uniform(-np.pi, +np.pi)
ang = qf.fubini_study_angle(qf.I(0).tensor, qf.Rx(theta, 0).su().tensor)
assert np.isclose(2 * ang / abs(theta), 1.0)
ang = qf.fubini_study_angle(qf.I(0).tensor, qf.Ry(theta, 0).tensor)
assert np.isclose(2 * ang / abs(theta), 1.0)
ang = qf.fubini_study_angle(qf.I(0).tensor, qf.Rz(theta, 0).tensor)
assert np.isclose(2 * ang / abs(theta), 1.0)
ang = qf.fubini_study_angle(qf.Swap(0, 1).tensor, qf.PSwap(theta, 0, 1).tensor)
assert np.isclose(2 * ang / abs(theta), 1.0)
ang = qf.fubini_study_angle(qf.I(0).tensor, qf.PhaseShift(theta, 0).tensor)
assert np.isclose(2 * ang / abs(theta), 1.0)
assert qf.fubini_study_close(qf.Rz(theta, 0).tensor, qf.Rz(theta, 0).tensor)
for n in range(1, 6):
eye = qf.IdentityGate(list(range(n)))
assert np.isclose(qf.fubini_study_angle(eye.tensor, eye.tensor), 0.0)
with pytest.raises(ValueError):
qf.fubini_study_angle(qf.RandomGate([1]).tensor, qf.RandomGate([0, 1]).tensor)
def fit_zyz(target_gate):
"""
Tensorflow example. Given an arbitrary one-qubit gate, use gradient
descent to find corresponding parameters of a universal ZYZ gate.
"""
assert bk.BACKEND == 'tensorflow'
tf = bk.TL
steps = 4000
t = tf.get_variable('t', [3])
gate = qf.ZYZ(t[0], t[1], t[2])
ang = qf.fubini_study_angle(target_gate.vec, gate.vec)
opt = tf.train.AdamOptimizer(learning_rate=0.001)
train = opt.minimize(ang, var_list=[t])
with tf.Session() as sess:
init_op = tf.global_variables_initializer()
sess.run(init_op)
for step in range(steps):
sess.run(train)
loss = sess.run(ang)
sys.stdout.write('\r')
sys.stdout.write("step: {} gate_angle: {}".format(step, loss))
if loss < 0.0001:
break
print()
return sess.run(t)
def test_fubini_study_angle_states() -> None:
# The state angle is half angle in Bloch sphere
angle1 = 0.1324
ket1 = qf.zero_state(1)
ket2 = qf.Rx(angle1, 0).run(ket1)
angle2 = qf.fubini_study_angle(ket1.tensor, ket2.tensor)
assert np.isclose(angle1, angle2 * 2)
def test_fidelity() -> None:
rho0 = qf.random_density(4)
rho1 = qf.random_density(4)
fid = qf.fidelity(rho0, rho1)
assert 0.0 <= fid <= 1.0
rho2 = qf.random_density([3, 2, 1, 0])
fid = qf.fidelity(rho0, rho2)
assert 0.0 <= fid <= 1.0
fid = qf.fidelity(rho0, rho0)
assert np.isclose(fid, 1.0)
ket0 = qf.random_state(3)
ket1 = qf.random_state(3)
fid0 = qf.state_fidelity(ket0, ket1)
rho0 = ket0.asdensity()
rho1 = ket1.asdensity()
fid1 = qf.fidelity(rho0, rho1)
assert np.isclose(fid1, fid0)
fid2 = np.cos(qf.fubini_study_angle(ket0.tensor, ket1.tensor)) ** 2
assert np.isclose(fid2, fid0)
def test_fidelity():
rho0 = qf.random_density(4)
rho1 = qf.random_density(4)
fid = qf.fidelity(rho0, rho1)
print('FID', fid)
assert 0.0 <= fid <= 1.0
rho2 = qf.random_density([3, 2, 1, 0])
fid = qf.fidelity(rho0, rho2)
assert 0.0 <= fid <= 1.0
fid = qf.fidelity(rho0, rho0)
print('FID', fid)
assert fid == ALMOST_ONE
ket0 = qf.random_state(3)
ket1 = qf.random_state(3)
fid0 = qf.state_fidelity(ket0, ket1)
rho0 = ket0.asdensity()
rho1 = ket1.asdensity()
fid1 = qf.fidelity(rho0, rho1)
assert qf.asarray(fid1 - fid0) == ALMOST_ZERO
fid2 = bk.cos(qf.fubini_study_angle(ket0.vec, ket1.vec))**2
assert qf.asarray(fid2 - fid0) == ALMOST_ZERO
def test_fubini_study_angle_states():
# The state angle is half angle in Bloch sphere
angle1 = 0.1324
ket1 = qf.zero_state(1)
ket2 = qf.RX(angle1, 0).run(ket1)
angle2 = qf.asarray(qf.fubini_study_angle(ket1.vec, ket2.vec))
assert angle1 - angle2 * 2 == ALMOST_ZERO
def test_bures_angle() -> None:
rho = qf.random_density(4)
assert np.isclose(qf.bures_angle(rho, rho), 0.0, atol=ATOL * 10)
rho1 = qf.random_density(4)
qf.bures_angle(rho, rho1)
ket0 = qf.random_state(4)
ket1 = qf.random_state(4)
rho0 = ket0.asdensity()
rho1 = ket1.asdensity()
ang0 = qf.fubini_study_angle(ket0.tensor, ket1.tensor)
ang1 = qf.bures_angle(rho0, rho1)
assert np.isclose(ang0, ang1)
def test_bures_angle():
rho = qf.random_density(4)
assert qf.bures_angle(rho, rho) == ALMOST_ZERO
rho1 = qf.random_density(4)
qf.bures_angle(rho, rho1)
ket0 = qf.random_state(4)
ket1 = qf.random_state(4)
rho0 = ket0.asdensity()
rho1 = ket1.asdensity()
ang0 = qf.fubini_study_angle(ket0.vec, ket1.vec)
ang1 = qf.bures_angle(rho0, rho1)
assert np.isclose(ang0, ang1)
def loss_fn():
"""Loss"""
gate = qf.ZYZ(t[0], t[1], t[2])
ang = qf.fubini_study_angle(target_gate.vec, gate.vec)
return ang