def test_singular_values_random4x4(self):
"""Tests computing the singular values for random 4 x 4 matrices."""
for _ in range(10):
matrix = np.random.randn(4, 4)
matrix += matrix.conj().T
qsve = QSVE(matrix)
print("Matrix:")
print(matrix)
sigmas = qsve.singular_values_classical()
print("Sigmas:", sigmas)
n = 6
qsigmas = qsve.top_singular_values(nprecision_bits=n,
init_state_row_and_col=None,
shots=50000,
ntop=4)
print("QSigmas:", qsigmas)
print("Max theory error:", qsve.max_error(n))
self.assertTrue(
qsve.has_value_close_to_singular_values(
qsigmas, qsve.max_error(n)))
print("Success!\n\n")
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_singular_values_identity8(self):
"""Tests QSVE gets close to the correct singular values for the 8 x 8 identity matrix."""
qsve = QSVE(np.identity(8))
sigma = max(qsve.singular_values_classical())
for n in range(3, 7):
qsigma = qsve.top_singular_values(nprecision_bits=n,
init_state_row_and_col=None,
shots=50000,
ntop=3)
self.assertTrue(abs(sigma - qsigma[0]) < qsve.max_error(n))
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))