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_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, diags, tlist = dec.rectangular(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_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.rectangular(A)