def test_random_unitary(self, tol):
"""This test checks the rectangular decomposition for a random unitary.
A random unitary is drawn from the Haar measure, then is decomposed via
the rectangular decomposition of Clements et al., and the resulting
beamsplitters are multiplied together. Test passes if the product
matches the drawn unitary.
"""
# TODO: this test currently uses the T and Ti functions used to compute
# Clements as the comparison. Probably should be changed.
n = 20
U = haar_measure(n)
tilist, tlist, diags = dec.clements(U)
qrec = np.identity(n)
for i in tilist:
qrec = dec.T(*i) @ qrec
qrec = np.diag(diags) @ qrec
for i in reversed(tlist):
qrec = dec.Ti(*i) @ qrec
assert np.allclose(U, qrec, atol=tol, rtol=0)
def test_decomposition(self, tol):
"""Test that an interferometer is correctly decomposed"""
n = 3
prog = sf.Program(n)
U = random_interferometer(n)
BS1, BS2, R = dec.clements(U)
G = ops.Interferometer(U)
cmds = G.decompose(prog.register)
S = np.identity(2 * n)
# calculating the resulting decomposed symplectic
for cmd in cmds:
# all operations should be BSgates or Rgates
assert isinstance(cmd.op, (ops.BSgate, ops.Rgate))
# build up the symplectic transform
modes = [i.ind for i in cmd.reg]
if isinstance(cmd.op, ops.Rgate):
S = _rotation(cmd.op.p[0].x, modes, n) @ S
if isinstance(cmd.op, ops.BSgate):
S = _beamsplitter(cmd.op.p[0].x, cmd.op.p[1].x, modes, n) @ S
# the resulting applied unitary
X1 = S[:n, :n]
P1 = S[n:, :n]
U_applied = X1 + 1j * P1
assert np.allclose(U, U_applied, atol=tol, rtol=0)
def test_clements_identity(self):
n = 20
U = np.identity(n)
(tilist, tlist, diags) = dec.clements(U)
qrec = np.identity(n)
for i in tilist:
qrec = dec.T(*i) @ qrec
qrec = np.diag(diags) @ qrec
for i in reversed(tlist):
qrec = dec.Ti(*i) @ qrec
self.assertAllAlmostEqual(U, qrec, delta=self.tol)
def test_clements_random_unitary(self):
error = np.empty(nsamples)
for k in range(nsamples):
n = 20
V = haar_measure(n)
(tilist, tlist, diags) = dec.clements(V)
qrec = np.identity(n)
for i in tilist:
qrec = dec.T(*i) @ qrec
qrec = np.diag(diags) @ qrec
for i in reversed(tlist):
qrec = dec.Ti(*i) @ qrec
error[k] = np.linalg.norm(V - qrec)
self.assertAlmostEqual(error.mean(), 0)
def test_clements_identity(self):
"""This test checks the rectangular decomposition for an identity unitary.
An identity unitary is decomposed via the rectangular decomposition of
Clements et al. and the resulting beamsplitters are multiplied together.
Test passes if the product matches identity.
"""
self.logTestName()
n = 20
U = np.identity(n)
(tilist, tlist, diags) = dec.clements(U)
qrec = np.identity(n)
for i in tilist:
qrec = dec.T(*i) @ qrec
qrec = np.diag(diags) @ qrec
for i in reversed(tlist):
qrec = dec.Ti(*i) @ qrec
self.assertAllAlmostEqual(U, qrec, delta=self.tol)
def test_clements_random_unitary(self):
"""This test checks the rectangular decomposition for a random unitary.
A random unitary is drawn from the Haar measure, then is decomposed via
the rectangular decomposition of Clements et al., and the resulting
beamsplitters are multiplied together. Test passes if the product
matches the drawn unitary.
"""
self.logTestName()
error = np.empty(nsamples)
for k in range(nsamples):
n = 20
V = haar_measure(n)
(tilist, tlist, diags) = dec.clements(V)
qrec = np.identity(n)
for i in tilist:
qrec = dec.T(*i) @ qrec
qrec = np.diag(diags) @ qrec
for i in reversed(tlist):
qrec = dec.Ti(*i) @ qrec
error[k] = np.linalg.norm(V - qrec)
self.assertAlmostEqual(error.mean(), 0)
def test_unitary_validation(self):
"""Test that an exception is raised if not unitary"""
A = np.random.random([5, 5]) + 1j * np.random.random([5, 5])
with pytest.raises(ValueError, match="matrix is not unitary"):
dec.clements(A)
