def prepare_gaussian_state(self, r, V, modes):
if isinstance(modes, int):
modes = [modes]
# make sure number of modes matches shape of r and V
N = len(modes)
if len(r) != 2 * N:
raise ValueError("Length of means vector must be twice the number of modes.")
if V.shape != (2 * N, 2 * N):
raise ValueError(
"Shape of covariance matrix must be [2N, 2N], where N is the number of modes."
)
# Include these lines to accommodate out of order modes, e.g.[1,0]
ordering = np.append(np.argsort(modes), np.argsort(modes) + len(modes))
V = V[ordering, :][:, ordering]
r = r[ordering]
# convert xp-ordering to symmetric ordering
means = np.vstack([r[:N], r[N:]]).reshape(-1, order="F")
C = changebasis(N)
cov = C @ V @ C.T
self.circuit.from_covmat(cov, modes)
self.circuit.from_mean(means, modes)
def prepare_gaussian_state(self, r, V, modes):
r"""Prepare the given Gaussian state (via the provided vector of
means and the covariance matrix) in the specified modes.
The requested mode(s) is/are traced out and replaced with the given Gaussian state.
Args:
r (array): the vector of means in xp ordering.
V (array): the covariance matrix in xp ordering.
modes (int or Sequence[int]): which mode to prepare the state in
If the modes are not sorted, this is take into account when preparing the state.
i.e., when a two mode state is prepared in modes=[3,1], then the first
mode of state goes into mode 3 and the second mode goes into mode 1 of the simulator.
"""
if isinstance(modes, int):
modes = [modes]
# make sure number of modes matches shape of r and V
N = len(modes)
if len(r) != 2 * N:
raise ValueError(
"Length of means vector must be twice the number of modes.")
if V.shape != (2 * N, 2 * N):
raise ValueError(
"Shape of covariance matrix must be [2N, 2N], where N is the number of modes."
)
# convert xp-ordering to symmetric ordering
means = vstack([r[:N], r[N:]]).reshape(-1, order='F')
C = changebasis(N)
cov = C @ V @ C.T
self.circuit.fromscovmat(cov, modes)
self.circuit.fromsmean(means, modes)
def test_three_mode_arbitrary(self):
"""Test that the correct result is returned for an arbitrary quadratic polynomial"""
self.logTestName()
A = np.array([[ 0.7086495 , -0.39299695, 0.30536448, 0.48822049, 0.64987373, 0.7020327 ],
[-0.39299695, 0.0284145 , 0.53202656, 0.20232385, 0.26288656, 0.20772833],
[ 0.30536448, 0.53202656, 0.28126466, 0.64192545, -0.36583748, 0.51704656],
[ 0.48822049, 0.20232385, 0.64192545, 0.51033017, 0.29129713, 0.77103581],
[ 0.64987373, 0.26288656, -0.36583748, 0.29129713, 0.37646972, 0.2383589 ],
[ 0.7020327 , 0.20772833, 0.51704656, 0.77103581, 0.2383589 ,-0.96494418]])
d = np.array([ 0.71785224, -0.80064627, 0.08799823, 0.76189805, 0.99665321, -0.60777437])
k = 0.123
self.circuit.reset(pure=self.kwargs['pure'])
a_list = [0.044+0.023j, 0.0432+0.123j, -0.12+0.04j]
r_list = [0.1065, 0.032, -0.123]
phi_list = [0.897, 0.31, 0.432]
mu = np.zeros([6])
cov = np.zeros([6, 6])
# squeeze and displace each mode
for i, (a_, r_, phi_) in enumerate(zip(a_list, r_list, phi_list)):
self.circuit.prepare_displaced_squeezed_state(a_, r_, phi_, i)
mu[2*i:2*i+2] = R(self.qphi).T @ np.array([a_.real, a_.imag]) * np.sqrt(2*self.hbar)
cov[2*i:2*i+2, 2*i:2*i+2] = R(self.qphi).T @ squeezed_cov(r_, phi_, hbar=self.hbar) @ R(self.qphi)
# apply a beamsplitter to the modes
self.circuit.beamsplitter(1/np.sqrt(2), 1/np.sqrt(2), 0, 1)
self.circuit.beamsplitter(1/np.sqrt(2), 1/np.sqrt(2), 1, 2)
state = self.circuit.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=self.qphi)
# apply a beamsplitter to vector of means and covariance matrices
t = 1/np.sqrt(2)
BS = np.array([[ t, 0, -t, 0],
[ 0, t, 0, -t],
[ t, 0, t, 0],
[ 0, t, 0, t]])
S1 = block_diag(BS, np.identity(2))
S2 = block_diag(np.identity(2), BS)
C = changebasis(3)
mu = C.T @ S2 @ S1 @ mu
cov = C.T @ S2 @ S1 @ cov @ S1.T @ S2.T @ C
modes = list(np.arange(6).reshape(2,-1).T)
mean_ex = np.trace(A @ cov) + mu @ A @ mu + mu @ d + k
var_ex = 2*np.trace(A @ cov @ A @ cov) + 4*mu.T @ A.T @ cov @ A @ mu + d.T @ cov @ d \
+ 2*mu.T @ A.T @ cov @ d + 2*d.T @ cov @ A @ mu \
- np.sum([np.linalg.det(self.hbar*A[:, m][n]) for m in modes for n in modes])
self.assertAlmostEqual(mean, mean_ex, delta=self.tol)
self.assertAlmostEqual(var, var_ex, delta=self.tol)
def test_means_changebasis(self):
"""Test the change of basis function applied to vectors. This function
converts from xp to symmetric ordering, and vice versa."""
C = so.changebasis(3)
means_xp = [1, 2, 3, 4, 5, 6]
means_symmetric = [1, 4, 2, 5, 3, 6]
assert np.all(C @ means_xp == means_symmetric)
assert np.all(C.T @ means_symmetric == means_xp)
def test_cov_changebasis(self):
"""Test the change of basis function applied to matrices. This function
converts from xp to symmetric ordering, and vice versa."""
C = so.changebasis(2)
cov_xp = np.array(
[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]]
)
cov_symmetric = np.array(
[[0, 2, 1, 3], [8, 10, 9, 11], [4, 6, 5, 7], [12, 14, 13, 15]]
)
assert np.all(C @ cov_xp @ C.T == cov_symmetric)
assert np.all(C.T @ cov_symmetric @ C == cov_xp)
def test_rotated_squeezed(self, setup_eng, hbar, tol):
"""Testing a rotated squeezed state"""
eng, prog = setup_eng(3)
r = 0.1
phi = 0.2312
v1 = (hbar / 2) * np.diag([np.exp(-r), np.exp(r)])
A = changebasis(3)
cov = A.T @ block_diag(*[rot(phi) @ v1 @ rot(phi).T] * 3) @ A
with prog.context as q:
ops.Gaussian(cov, decomp=False) | q
state = eng.run(prog).state
assert np.allclose(state.cov(), cov, atol=tol)
def test_covariance_rotated_squeezed(self):
self.logTestName()
q = self.eng.register
r = 0.1
phi = 0.2312
v1 = (self.hbar / 2) * np.diag([np.exp(-r), np.exp(r)])
A = changebasis(3)
cov = A.T @ block_diag(*[rot(phi) @ v1 @ rot(phi).T] * 3) @ A
with self.eng:
Gaussian(cov, decomp=False) | q
state = self.eng.run()
self.assertAllAlmostEqual(state.cov(), cov, delta=self.tol)
def test_rotated_squeezed(self, setup_eng, hbar, tol):
"""Testing decomposed rotated squeezed state"""
eng, q = setup_eng(3)
r = 0.1
phi = 0.2312
v1 = (hbar / 2) * np.diag([np.exp(-r), np.exp(r)])
A = changebasis(3)
cov = A.T @ block_diag(*[rot(phi) @ v1 @ rot(phi).T] * 3) @ A
with eng:
ops.Gaussian(cov) | q
state = eng.run()
assert np.allclose(state.cov(), cov, atol=tol)
assert np.all(len(eng.cmd_applied[0]) == 3)
def test_covariance_rotated_squeezed(self):
self.eng.reset()
q = self.eng.register
r = 0.1
phi = 0.2312
v1 = (self.hbar / 2) * np.diag([np.exp(-r), np.exp(r)])
A = changebasis(3)
cov = A.T @ block_diag(*[rot(phi) @ v1 @ rot(phi).T] * 3) @ A
with self.eng:
CovarianceState(cov) | q
state = self.eng.run(backend=self.backend_name, cutoff_dim=self.D)
self.assertAllAlmostEqual(state.cov(), cov, delta=self.tol)
self.assertAllEqual(len(self.eng.cmd_applied), 3)
def prepare_gaussian_state(self, r, V, modes):
if isinstance(modes, int):
modes = [modes]
# make sure number of modes matches shape of r and V
N = len(modes)
if len(r) != 2*N:
raise ValueError("Length of means vector must be twice the number of modes.")
if V.shape != (2*N, 2*N):
raise ValueError("Shape of covariance matrix must be [2N, 2N], where N is the number of modes.")
# convert xp-ordering to symmetric ordering
means = vstack([r[:N], r[N:]]).reshape(-1, order='F')
C = changebasis(N)
cov = C @ V @ C.T
self.circuit.fromscovmat(cov, modes)
self.circuit.fromsmean(means, modes)
def test_rotated_squeezed(self, setup_eng, cutoff, hbar, tol):
eng, q = setup_eng(3)
r = 0.1
phi = 0.2312
in_state = squeezed_state(r, phi, basis="fock", fock_dim=cutoff)
v1 = (hbar / 2) * np.diag([np.exp(-2 * r), np.exp(2 * r)])
A = changebasis(3)
cov = A.T @ block_diag(*[rot(phi) @ v1 @ rot(phi).T] * 3) @ A
with eng:
ops.Gaussian(cov) | q
state = eng.run()
assert len(eng.cmd_applied[0]) == 3
for n in range(3):
assert np.allclose(state.fidelity(in_state, n), 1, atol=tol)
def test_covariance_rotated_squeezed(self):
self.logTestName()
q = self.eng.register
r = 0.1
phi = 0.2312
in_state = squeezed_state(r, phi, basis='fock', fock_dim=self.D)
v1 = (self.hbar / 2) * np.diag([np.exp(-2 * r), np.exp(2 * r)])
A = changebasis(3)
cov = A.T @ block_diag(*[rot(phi) @ v1 @ rot(phi).T] * 3) @ A
with self.eng:
Gaussian(cov) | q
state = self.eng.run(**self.kwargs)
self.assertAllEqual(len(self.eng.cmd_applied[0]), 3)
for n in range(3):
self.assertAllAlmostEqual(state.fidelity(in_state, n),
1,
delta=self.tol)
def test_three_mode_arbitrary(self, setup_backend, pure, hbar, tol):
"""Test that the correct result is returned for an arbitrary quadratic polynomial"""
backend = setup_backend(3)
# increase the cutoff to 7 for accuracy
backend.reset(cutoff_dim=7, pure=pure)
# fmt:off
A = np.array([[
0.7086495, -0.39299695, 0.30536448, 0.48822049, 0.64987373,
0.7020327
],
[
-0.39299695, 0.0284145, 0.53202656, 0.20232385,
0.26288656, 0.20772833
],
[
0.30536448, 0.53202656, 0.28126466, 0.64192545,
-0.36583748, 0.51704656
],
[
0.48822049, 0.20232385, 0.64192545, 0.51033017,
0.29129713, 0.77103581
],
[
0.64987373, 0.26288656, -0.36583748, 0.29129713,
0.37646972, 0.2383589
],
[
0.7020327, 0.20772833, 0.51704656, 0.77103581,
0.2383589, -0.96494418
]])
# fmt:on
d = np.array([
0.71785224, -0.80064627, 0.08799823, 0.76189805, 0.99665321,
-0.60777437
])
k = 0.123
a_list = [0.044 + 0.023j, 0.0432 + 0.123j, -0.12 + 0.04j]
r_list = [0.1065, 0.032, -0.123]
phi_list = [0.897, 0.31, 0.432]
mu = np.zeros([6])
cov = np.zeros([6, 6])
# squeeze and displace each mode
for i, (a_, r_, phi_) in enumerate(zip(a_list, r_list, phi_list)):
backend.prepare_displaced_squeezed_state(np.abs(a_), np.angle(a_),
r_, phi_, i)
mu[2 * i:2 * i + 2] = (R(qphi).T @ np.array([a_.real, a_.imag]) *
np.sqrt(2 * hbar))
cov[2 * i:2 * i + 2, 2 * i:2 * i + 2] = (
R(qphi).T @ utils.squeezed_cov(r_, phi_, hbar=hbar) @ R(qphi))
# apply a beamsplitter to the modes
backend.beamsplitter(np.pi / 4, 0.0, 0, 1)
backend.beamsplitter(np.pi / 4, 0.0, 1, 2)
state = backend.state()
mean, var = state.poly_quad_expectation(A, d, k, phi=qphi)
# apply a beamsplitter to vector of means and covariance matrices
t = 1 / np.sqrt(2)
BS = np.array([[t, 0, -t, 0], [0, t, 0, -t], [t, 0, t, 0],
[0, t, 0, t]])
S1 = block_diag(BS, np.identity(2))
S2 = block_diag(np.identity(2), BS)
C = changebasis(3)
mu = C.T @ S2 @ S1 @ mu
cov = C.T @ S2 @ S1 @ cov @ S1.T @ S2.T @ C
modes = list(np.arange(6).reshape(2, -1).T)
mean_ex = np.trace(A @ cov) + mu @ A @ mu + mu @ d + k
var_ex = (2 * np.trace(A @ cov @ A @ cov) +
4 * mu.T @ A.T @ cov @ A @ mu + d.T @ cov @ d +
2 * mu.T @ A.T @ cov @ d + 2 * d.T @ cov @ A @ mu - np.sum([
np.linalg.det(hbar * A[:, m][n]) for m in modes
for n in modes
]))
assert np.allclose(mean, mean_ex, atol=tol, rtol=0)
assert np.allclose(var, var_ex, atol=tol, rtol=0)
