def test_sf_ordering_in_fock_tensor(tol):
"""Test that the reordering works when using sf_order=True"""
cutoff = 5
nmodes = 2
s = np.arcsinh(1.0)
phi = np.pi / 6
alphas = np.zeros([nmodes])
S = two_mode_squeezing(s, phi)
T = fock_tensor(S, alphas, cutoff)
Tsf = fock_tensor(S, alphas, cutoff, sf_order=True)
assert np.allclose(T.transpose([0, 2, 1, 3]), Tsf, atol=tol, rtol=0)
def test_single_mode_identity(choi_r, tol):
"""Tests the correct construction of the single mode identity operation"""
nmodes = 1
cutoff = 7
S = np.identity(2 * nmodes)
alphas = np.zeros([nmodes])
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
expected = np.identity(cutoff)
assert np.allclose(T, expected, atol=tol, rtol=0)
def test_single_mode_rotation(choi_r, tol):
"""Tests the correct construction of the single mode rotation operation"""
nmodes = 1
cutoff = 7
theta = 2 * np.pi * np.random.rand()
S = rotation(theta)
alphas = np.zeros([nmodes])
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
expected = np.diag(np.exp(1j * theta * np.arange(cutoff)))
assert np.allclose(T, expected, atol=tol, rtol=0)
def test_hong_ou_mandel_interference(choi_r, phi, tol):
r"""Tests Hong-Ou-Mandel interference for a 50:50 beamsplitter.
If one writes :math:`U` for the Fock representation of a 50-50 beamsplitter
then it must hold that :math:`\langle 1,1|U|1,1 \rangle = 0`.
"""
S = beam_splitter(np.pi / 4, phi) # a 50-50 beamsplitter with phase phi
cutoff = 2
nmodes = 2
alphas = np.zeros([nmodes])
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
assert np.allclose(T[1, 1, 1, 1], 0.0, atol=tol, rtol=0)
def test_interferometer_selection_rules(choi_r, nmodes, tol):
r"""Test the selection rules of an interferometer.
If one writes the interferometer gate of k modes as :math:`U` and its matrix elements as
:math:`\langle p_0 p_1 \ldots p_{k-1} |U|q_0 q_1 \ldots q_{k-1}\rangle` then these elements
are nonzero if and only if :math:`\sum_{i=0}^k p_i = \sum_{i=0}^k q_i`. This test checks
that this selection rule holds.
"""
U = random_interferometer(nmodes)
S = interferometer(U)
alphas = np.zeros([nmodes])
cutoff = 4
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
for p in product(list(range(cutoff)), repeat=nmodes):
for q in product(list(range(cutoff)), repeat=nmodes):
if sum(p) != sum(q): # Check that there are the same total number of photons in the bra and the ket
r = tuple(list(p) + list(q))
assert np.allclose(T[r], 0.0, atol=tol, rtol=0)
def test_two_mode_squeezing(choi_r, tol):
r"""Tests the selection rules of a two mode squeezing operation.
If one writes the squeezing gate as :math:`S_2` and its matrix elements as
:math:`\langle p_0 p_1|S_2|q_0 q_1 \rangle` then these elements are nonzero
if and only if :math:`p_0 - q_0 = p_1 - q_1`. This test checks that this
selection rule holds.
"""
cutoff = 5
nmodes = 2
s = np.arcsinh(1.0)
phi = np.pi / 6
alphas = np.zeros([nmodes])
S = two_mode_squeezing(s, phi)
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
for p in product(list(range(cutoff)), repeat=nmodes):
for q in product(list(range(cutoff)), repeat=nmodes):
if p[0] - q[0] != p[1] - q[1]:
t = tuple(list(p) + list(q))
assert np.allclose(T[t], 0, atol=tol, rtol=0)
def test_single_mode_displacement(choi_r, tol):
"""Tests the correct construction of the single mode displacement operation"""
nmodes = 1
cutoff = 5
alphas = (0.3 + 0.5 * 1j) * np.ones([nmodes])
S = np.identity(2 * nmodes)
# This data is obtained by using qutip
# np.array(displace(40,alpha).data.todense())[0:5,0:5]
expected = np.array(
[
[0.84366482 + 0.00000000e00j, -0.25309944 + 4.21832408e-01j, -0.09544978 - 1.78968334e-01j, 0.06819609 + 3.44424719e-03j, -0.01109048 + 1.65323865e-02j,],
[0.25309944 + 4.21832408e-01j, 0.55681878 + 0.00000000e00j, -0.29708743 + 4.95145724e-01j, -0.14658716 - 2.74850926e-01j, 0.12479885 + 6.30297236e-03j,],
[-0.09544978 + 1.78968334e-01j, 0.29708743 + 4.95145724e-01j, 0.31873657 + 0.00000000e00j, -0.29777767 + 4.96296112e-01j, -0.18306015 - 3.43237787e-01j,],
[-0.06819609 + 3.44424719e-03j, -0.14658716 + 2.74850926e-01j, 0.29777767 + 4.96296112e-01j, 0.12389162 + 1.10385981e-17j, -0.27646677 + 4.60777945e-01j,],
[-0.01109048 - 1.65323865e-02j, -0.12479885 + 6.30297236e-03j, -0.18306015 + 3.43237787e-01j, 0.27646677 + 4.60777945e-01j, -0.03277289 + 1.88440656e-17j,],
]
)
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
assert np.allclose(T, expected, atol=tol, rtol=0)
def test_single_mode_displacement_squeezing(choi_r, tol):
"""Tests the correct construction of the single mode squeezing operation followed by the single mode displacement operation"""
nmodes = 1
s = 1.0
cutoff = 5
S = squeezing(s, 0.0)
alphas = (0.5 + 0.4 * 1j) * np.ones([nmodes])
# This data is obtained by using qutip
# np.array((displace(40,alpha)*squeeze(40,r)).data.todense())[0:5,0:5]
expected = np.array(
[
[0.6263739 + 0.09615331j, -0.22788717 + 0.13121343j, 0.36548296 - 0.0200537j, -0.20708137 + 0.14004403j, 0.25645667 - 0.06275564j],
[0.5425389 + 0.14442404j, 0.19268911 + 0.15615312j, 0.11497303 + 0.13744549j, 0.21448948 + 0.08109308j, -0.03652914 + 0.15069359j],
[-0.00915607 + 0.07475267j, 0.48081922 + 0.10576742j, -0.00961086 + 0.20535144j, 0.33089303 + 0.09864247j, 0.02555522 + 0.19950786j],
[-0.34614367 - 0.05229875j, 0.11543956 + 0.01112537j, 0.16672961 + 0.07439407j, 0.02323121 + 0.15103267j, 0.27233637 + 0.08297028j],
[-0.14390852 - 0.08884069j, -0.37898007 - 0.07630228j, 0.12911863 - 0.08963054j, -0.12164023 + 0.04431394j, 0.1141808 + 0.01581529j],
]
)
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
assert np.allclose(T, expected, atol=tol, rtol=0)
def test_single_mode_squeezing(choi_r, tol):
"""Tests the correct construction of the single mode squeezing operation"""
nmodes = 1
s = 1.0
cutoff = 5
S = squeezing(s, 0.0)
alphas = np.zeros([nmodes])
# This data is obtained by using qutip
# np.array(squeeze(40,r).data.todense())[0:5,0:5]
expected = np.array(
[
[0.80501818 + 0.0j, 0.0 + 0.0j, 0.43352515 + 0.0j, 0.0 + 0.0j, 0.2859358 + 0.0j],
[0.0 + 0.0j, 0.52169547 + 0.0j, 0.0 + 0.0j, 0.48661591 + 0.0j, 0.0 + 0.0j],
[-0.43352515 + 0.0j, 0.0 + 0.0j, 0.10462138 + 0.0j, 0.0 + 0.0j, 0.29199268 + 0.0j],
[0.0 + 0.0j, -0.48661591 + 0.0j, 0.0 + 0.0j, -0.23479643 + 0.0j, 0.0 + 0.0j],
[0.2859358 + 0.0j, 0.0 + 0.0j, -0.29199268 + 0.0j, 0.0 + 0.0j, -0.34474749 + 0.0j],
]
)
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
assert np.allclose(T, expected, atol=tol, rtol=0)
def test_interferometer_single_excitation(choi_r, nmodes, tol):
r"""Test that the representation of an interferometer in the single
excitation manifold is precisely the unitary matrix that represents it
mode in space.
Let :math:`V` be a unitary matrix in N modes and let :math:`U` be its Fock representation
Also let :math:`|i \rangle = |0_0,\ldots, 1_i, 0_{N-1} \rangle`, i.e a single photon in mode :math:`i`.
Then it must hold that :math:`V_{i,j} = \langle i | U | j \rangle`.
"""
U = random_interferometer(nmodes)
S = interferometer(U)
alphas = np.zeros([nmodes])
cutoff = 2
T = fock_tensor(S, alphas, cutoff, choi_r=choi_r)
# Construct a list with all the indices corresponding to |i \rangle
vec_list = np.identity(nmodes, dtype=int).tolist()
# Calculate the matrix \langle i | U | j \rangle = T[i+j]
U_rec = np.empty([nmodes, nmodes], dtype=complex)
for i, vec_i in enumerate(vec_list):
for j, vec_j in enumerate(vec_list):
U_rec[i, j] = T[tuple(vec_i + vec_j)]
assert np.allclose(U_rec, U, atol=tol, rtol=0)