def test_merge(self, hbar, tol):
"""Test that two symplectics merge: S = S2 @ S1"""
n = 3
S1 = random_symplectic(n)
S2 = random_symplectic(n)
G1 = ops.GaussianTransform(S1)
G1inv = ops.GaussianTransform(np.linalg.inv(S1))
G2 = ops.GaussianTransform(S2)
# a symplectic merged with its inverse is identity
assert G1.merge(G1inv) is None
# two merged symplectics are the same as their product
assert np.allclose(G1.merge(G2).p[0].x, S2 @ S1, atol=tol, rtol=0)
def test_decomposition_passive(self, tol):
"""Test that a passive symplectic is correctly decomposed into an interferometer"""
n = 3
S = random_symplectic(n, passive=True)
X1 = S[:n, :n]
P1 = S[n:, :n]
U1 = X1 + 1j * P1
prog = sf.Program(n)
G = ops.GaussianTransform(S)
cmds = G.decompose(prog.register)
S = np.identity(2 * n)
# command queue should have 1 interferometer
assert len(cmds) == 1
# calculating the resulting decomposed symplectic
for cmd in cmds:
# all operations should be Interferometers
assert isinstance(cmd.op, ops.Interferometer)
# build up the symplectic transform
#modes = [i.ind for i in cmd.reg]
if isinstance(cmd.op, ops.Interferometer):
U1 = cmd.op.p[0]
S_U = np.vstack(
[np.hstack([U1.real, -U1.imag]), np.hstack([U1.imag, U1.real])]
)
S = S_U @ S
# the resulting covariance state
cov = S @ S.T
assert np.allclose(cov, S @ S.T, atol=tol, rtol=0)
def test_setting_hbar(self, hbar):
"""Test that an exception is raised if hbar not provided"""
prog = sf.Program(3, hbar=hbar)
S1 = random_symplectic(3, passive=False)
with pytest.raises(ValueError, match="specify the hbar keyword argument"):
ops.GaussianTransform(S1)
# hbar can be passed as a keyword arg
G = ops.GaussianTransform(S1, hbar=hbar)
assert G.hbar == hbar
# or determined via the engine context
with eng:
G = ops.GaussianTransform(S1)
assert G.hbar == hbar
def test_gaussian_transform(self, setup_eng, hbar, tol):
"""Test applying a Gaussian symplectic transform"""
eng, prog = setup_eng(3)
with prog.context as q:
ops.GaussianTransform(S) | q
state = eng.run(prog).state
assert np.allclose(state.cov(), S @ S.T * hbar / 2, atol=tol)
def test_passive(self, tol):
"""Test that a passive decomposition is correctly flagged as requiring
only a single interferometer"""
G = ops.GaussianTransform(np.identity(6))
assert not G.active
assert hasattr(G, "U1")
assert not hasattr(G, "Sq")
assert not hasattr(G, "U2")
def test_active_gaussian_transform_on_vacuum(self, setup_eng, hbar, tol):
"""Test applying a passive Gaussian symplectic transform,
which is simply squeezing and ONE interferometer"""
eng, prog = setup_eng(3)
with prog.context as q:
ops.GaussianTransform(S, vacuum=True) | q
state = eng.run(prog).state
assert np.allclose(state.cov(), S @ S.T * hbar / 2, atol=tol)
def test_active(self, tol):
"""Test that an active decomposition is correctly flagged as requiring
two interferometers and squeezing"""
S1 = random_symplectic(3, passive=False)
G = ops.GaussianTransform(S1)
assert G.active
assert hasattr(G, "U1")
assert hasattr(G, "Sq")
assert hasattr(G, "U2")
def test_decomposition_active(self, hbar, tol):
"""Test that an active symplectic is correctly decomposed into
two interferometers and squeezing"""
n = 3
S = random_symplectic(n, passive=False)
O1, Sq, O2 = dec.bloch_messiah(S)
X1 = O1[:n, :n]
P1 = O1[n:, :n]
X2 = O2[:n, :n]
P2 = O2[n:, :n]
U1 = X1 + 1j * P1
U2 = X2 + 1j * P2
prog = sf.Program(n, hbar=hbar)
with eng:
G = ops.GaussianTransform(S)
cmds = G.decompose(q)
assert np.all(U1 == G.U1)
assert np.all(U2 == G.U2)
assert np.all(np.diag(Sq)[:n] == G.Sq)
S = np.identity(2 * n)
# command queue should have 2 interferometers, 3 squeezers
assert len(cmds) == 5
# calculating the resulting decomposed symplectic
for cmd in cmds:
# all operations should be BSgates, Rgates, or Sgates
assert isinstance(cmd.op, (ops.Interferometer, ops.Sgate))
# build up the symplectic transform
modes = [i.ind for i in cmd.reg]
if isinstance(cmd.op, ops.Sgate):
S = _squeezing(cmd.op.p[0].x, cmd.op.p[1].x, modes, n) @ S
if isinstance(cmd.op, ops.Interferometer):
U1 = cmd.op.p[0].x
S_U = np.vstack([
np.hstack([U1.real, -U1.imag]),
np.hstack([U1.imag, U1.real])
])
S = S_U @ S
# the resulting covariance state
cov = S @ S.T
assert np.allclose(cov, S @ S.T * hbar / 2, atol=tol, rtol=0)
def test_symplectic_composition(depth, width):
"""Tests that symplectic operations are composed correctly"""
eng = sf.LocalEngine(backend="gaussian")
eng1 = sf.LocalEngine(backend="gaussian")
circuit = sf.Program(width)
Snet = np.identity(2 * width)
with circuit.context as q:
for _ in range(depth):
S = random_symplectic(width, scale=0.2)
Snet = S @ Snet
ops.GaussianTransform(S) | q
compiled_circuit = circuit.compile(compiler="gaussian_unitary")
assert np.allclose(compiled_circuit.circuit[0].op.p[0], Snet)
def test_passive_gaussian_transform(self, setup_eng, tol):
"""Test applying a passive Gaussian symplectic transform,
which is simply an interferometer"""
eng, q = setup_eng(3)
O = np.vstack(
[np.hstack([u1.real, -u1.imag]),
np.hstack([u1.imag, u1.real])])
with eng:
ops.All(ops.Squeezed(0.5)) | q
init = eng.run()
ops.GaussianTransform(O) | q
state = eng.run()
assert np.allclose(state.cov(), O @ init.cov() @ O.T, atol=tol)
def test_active_on_vacuum(self, hbar, tol):
"""Test that an active symplectic applied to a vacuum is
correctly decomposed into just squeezing and one interferometer"""
n = 3
S = random_symplectic(n, passive=False)
O1, Sq, O2 = dec.bloch_messiah(S)
X1 = O1[:n, :n]
P1 = O1[n:, :n]
X2 = O2[:n, :n]
P2 = O2[n:, :n]
U1 = X1 + 1j * P1
U2 = X2 + 1j * P2
prog = sf.Program(n)
G = ops.GaussianTransform(S, vacuum=True)
cmds = G.decompose(prog.register)
S = np.identity(2 * n)
# command queue should have 3 Sgates, 1 interferometer
assert len(cmds) == 4
# calculating the resulting decomposed symplectic
for cmd in cmds:
# all operations should be Interferometers or Sgates
assert isinstance(cmd.op, (ops.Interferometer, ops.Sgate))
# build up the symplectic transform
modes = [i.ind for i in cmd.reg]
if isinstance(cmd.op, ops.Sgate):
S = _squeezing(cmd.op.p[0].x, cmd.op.p[1].x, modes, n) @ S
if isinstance(cmd.op, ops.Interferometer):
U1 = cmd.op.p[0].x
S_U = np.vstack([
np.hstack([U1.real, -U1.imag]),
np.hstack([U1.imag, U1.real])
])
S = S_U @ S
# the resulting covariance state
cov = S @ S.T
assert np.allclose(cov, S @ S.T, atol=tol, rtol=0)
def compile(self, seq, registers):
"""Try to arrange a quantum circuit into the canonical Symplectic form.
This method checks whether the circuit can be implemented as a sequence of Gaussian operations.
If the answer is yes it arranges them in the canonical order with displacement at the end.
Args:
seq (Sequence[Command]): quantum circuit to modify
registers (Sequence[RegRefs]): quantum registers
Returns:
List[Command]: modified circuit
Raises:
CircuitError: the circuit does not correspond to a Gaussian unitary
"""
# Check which modes are actually being used
used_modes = []
for operations in seq:
modes = [modes_label.ind for modes_label in operations.reg]
used_modes.append(modes)
# pylint: disable=consider-using-set-comprehension
used_modes = list(
set([item for sublist in used_modes for item in sublist]))
# dictionary mapping the used modes to consecutive non-negative integers
dict_indices = {used_modes[i]: i for i in range(len(used_modes))}
nmodes = len(used_modes)
# This is the identity transformation in phase-space, multiply by the identity and add zero
Snet = np.identity(2 * nmodes)
rnet = np.zeros(2 * nmodes)
# Now we will go through each operation in the sequence `seq` and apply it in quadrature space
# We will keep track of the net transforation in the Symplectic matrix `Snet` and the quadrature
# vector `rnet`.
for operations in seq:
name = operations.op.__class__.__name__
params = par_evaluate(operations.op.p)
modes = [modes_label.ind for modes_label in operations.reg]
if name == "Dgate":
rnet = rnet + expand_vector(
params[0] *
(np.exp(1j * params[1])), dict_indices[modes[0]], nmodes)
else:
if name == "Rgate":
S = expand(rotation(params[0]), dict_indices[modes[0]],
nmodes)
elif name == "Sgate":
S = expand(squeezing(params[0], params[1]),
dict_indices[modes[0]], nmodes)
elif name == "S2gate":
S = expand(
two_mode_squeezing(params[0], params[1]),
[dict_indices[modes[0]], dict_indices[modes[1]]],
nmodes,
)
elif name == "Interferometer":
S = expand(interferometer(params[0]),
[dict_indices[mode] for mode in modes], nmodes)
elif name == "GaussianTransform":
S = expand(params[0],
[dict_indices[mode] for mode in modes], nmodes)
elif name == "BSgate":
S = expand(
beam_splitter(params[0], params[1]),
[dict_indices[modes[0]], dict_indices[modes[1]]],
nmodes,
)
elif name == "MZgate":
v = np.exp(1j * params[0])
u = np.exp(1j * params[1])
U = 0.5 * np.array([[u * (v - 1), 1j *
(1 + v)], [1j * u * (1 + v), 1 - v]])
S = expand(
interferometer(U),
[dict_indices[modes[0]], dict_indices[modes[1]]],
nmodes,
)
Snet = S @ Snet
rnet = S @ rnet
# Having obtained the net displacement we simply convert it into complex notation
alphas = 0.5 * (rnet[0:nmodes] + 1j * rnet[nmodes:2 * nmodes])
# And now we just pass the net transformation as a big Symplectic operation plus displacements
ord_reg = [r for r in list(registers) if r.ind in used_modes]
ord_reg = sorted(list(ord_reg), key=lambda x: x.ind)
if np.allclose(Snet, np.identity(2 * nmodes)):
A = []
else:
A = [Command(ops.GaussianTransform(Snet), ord_reg)]
B = [
Command(ops.Dgate(np.abs(alphas[i]), np.angle(alphas[i])),
ord_reg[i]) for i in range(len(ord_reg))
if not np.allclose(alphas[i], 0.0)
]
return A + B
