def test_unitary_evals_matrix_singular_values_identity_2by2(self):
"""Tests that the eigenvalues of the unitary are the matrix singular values."""
# Dimension of system
dim = 2
# Define the matrix and QSVE object
matrix = np.identity(dim)
qsve = QSVE(matrix)
# Get the (normalized) singular values of the matrix
sigmas = qsve.singular_values_classical(normalized=True)
# Get the eigenvalues of the QSVE unitary
evals, _ = np.linalg.eig(qsve.unitary())
# Make sure there are the correct number of eigenvalues
self.assertEqual(len(evals), dim**2)
qsigmas = []
for eval in evals:
qsigma = qsve.unitary_eval_to_singular_value(eval)
if qsigma not in qsigmas:
qsigmas.append(qsigma)
self.assertTrue(np.allclose(qsigmas, sigmas))
def test_unitary_conjugate_evals(self):
"""Tests that for each eigenvalue lambda of the unitary, lambda* is also an eigenvalue, as required."""
for _ in range(100):
matrix = np.random.randn(2, 2)
matrix += matrix.conj().T
qsve = QSVE(matrix)
umat = qsve.unitary()
evals, _ = np.linalg.eig(umat)
for eval in evals:
self.assertIn(np.conjugate(eval), evals)
def test_unitary(self):
"""Tests for the unitary used for QPE."""
for dim in [2, 4]:
for _ in range(50):
matrix = np.random.randn(dim, dim)
matrix += matrix.conj().T
qsve = QSVE(matrix)
unitary = qsve.unitary()
self.assertTrue(
np.allclose(unitary.conj().T @ unitary,
np.identity(dim**2)))
def test_unitary_evals_to_matrix_singular_vals(self):
"""Tests QSVE.unitary() by ensuring the eigenvalues of the unitary relate to the singular values of the
input matrix in the expected way.
"""
for _ in range(100):
matrix = np.random.randn(2, 2)
matrix += matrix.conj().T
qsve = QSVE(matrix)
sigmas = qsve.singular_values_classical(normalized=True)
umat = qsve.unitary()
evals, _ = np.linalg.eig(umat)
qsigmas = []
for eval in evals:
qsigma = qsve.unitary_eval_to_singular_value(eval)
qsigma = round(qsigma, 4)
if qsigma not in qsigmas:
qsigmas.append(qsigma)
self.assertTrue(
np.allclose(sorted(qsigmas), sorted(sigmas), atol=1e-3))
