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_rectangular(self, U, tol):
"""This test checks the function :func:`dec.rectangular` for
various unitary matrices.
A given unitary (identity or random draw from Haar measure) is
decomposed using the function :func:`dec.rectangular`
and the resulting beamsplitters are multiplied together.
Test passes if the product matches the given unitary.
"""
nmax, mmax = U.shape
assert nmax == mmax
tilist, diags, tlist = dec.rectangular(U)
qrec = np.identity(nmax)
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_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_random_unitary_phase_end(self, tol):
"""This test checks the rectangular decomposition with phases at the end.
A random unitary is drawn from the Haar measure, then is decomposed
using Eq. 5 of the rectangular decomposition procedure of Clements et al,
i.e., moving all the phases to the end of the interferometer. The
resulting beamsplitters are multiplied together. Test passes if the
product matches the drawn unitary.
"""
n = 20
U = haar_measure(n)
tlist, diags, _ = dec.rectangular_phase_end(U)
qrec = np.identity(n)
for i in tlist:
qrec = dec.T(*i) @ qrec
qrec = np.diag(diags) @ qrec
assert np.allclose(U, qrec, atol=tol, rtol=0)
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_clements_phase_end_random_unitary(self):
"""This test checks the rectangular decomposition with phases at the end.
A random unitary is drawn from the Haar measure, then is decomposed
using Eq. 5 of the rectangular decomposition procedure of Clements et al
, i.e., moving all the phases to the end of the interferometer. 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
U = haar_measure(n)
new_tlist, new_diags = dec.clements_phase_end(U)
U_rec = np.identity(n)
for i in new_tlist:
U_rec = dec.T(*i) @ U_rec
U_rec = np.diag(new_diags) @ U_rec
self.assertAlmostEqual(np.linalg.norm(U_rec - U),
0,
delta=self.tol)
