def test_random_operators_are_reproducible(self):
op1 = random_diagonal_coulomb_hamiltonian(5, seed=5947)
op2 = random_diagonal_coulomb_hamiltonian(5, seed=5947)
numpy.testing.assert_allclose(op1.one_body, op2.one_body)
numpy.testing.assert_allclose(op1.two_body, op2.two_body)
op1 = random_interaction_operator(5, seed=8911)
op2 = random_interaction_operator(5, seed=8911)
numpy.testing.assert_allclose(op1.one_body_tensor, op2.one_body_tensor)
numpy.testing.assert_allclose(op1.two_body_tensor, op2.two_body_tensor)
op1 = random_quadratic_hamiltonian(5, seed=17711)
op2 = random_quadratic_hamiltonian(5, seed=17711)
numpy.testing.assert_allclose(op1.combined_hermitian_part,
op2.combined_hermitian_part)
numpy.testing.assert_allclose(op1.antisymmetric_part,
op2.antisymmetric_part)
op1 = random_antisymmetric_matrix(5, seed=24074)
op2 = random_antisymmetric_matrix(5, seed=24074)
numpy.testing.assert_allclose(op1, op2)
op1 = random_hermitian_matrix(5, seed=56753)
op2 = random_hermitian_matrix(5, seed=56753)
numpy.testing.assert_allclose(op1, op2)
op1 = random_unitary_matrix(5, seed=56486)
op2 = random_unitary_matrix(5, seed=56486)
numpy.testing.assert_allclose(op1, op2)
def test_diagonalizing_bogoliubov_transform_exceptions(self):
quad_ham = random_quadratic_hamiltonian(5)
with self.assertRaises(ValueError):
_ = quad_ham.diagonalizing_bogoliubov_transform(spin_sector=0)
quad_ham = random_quadratic_hamiltonian(
5, conserves_particle_number=False, expand_spin=True)
with self.assertRaises(NotImplementedError):
_ = quad_ham.diagonalizing_bogoliubov_transform(spin_sector=0)
def test_random_quadratic(self):
n_qubits = 5
quad_ham = random_quadratic_hamiltonian(n_qubits, True)
ferm_op = get_fermion_operator(quad_ham)
self.assertTrue(
jordan_wigner(ferm_op) == jordan_wigner(
get_diagonal_coulomb_hamiltonian(ferm_op)))
def test_ground_state_particle_nonconserving(self):
"""Test getting the ground state preparation circuit for a Hamiltonian
that does not conserve particle number."""
for n_qubits in self.n_qubits_range:
# Initialize a particle-number-conserving Hamiltonian
quadratic_hamiltonian = random_quadratic_hamiltonian(
n_qubits, False, True)
# Compute the true ground state
sparse_operator = get_sparse_operator(quadratic_hamiltonian)
ground_energy, _ = get_ground_state(sparse_operator)
# Obtain the circuit
circuit_description, start_orbitals = (
gaussian_state_preparation_circuit(quadratic_hamiltonian))
# Initialize the starting state
state = jw_configuration_state(start_orbitals, n_qubits)
# Apply the circuit
particle_hole_transformation = (
jw_sparse_particle_hole_transformation_last_mode(n_qubits))
for parallel_ops in circuit_description:
for op in parallel_ops:
if op == 'pht':
state = particle_hole_transformation.dot(state)
else:
i, j, theta, phi = op
state = jw_sparse_givens_rotation(
i, j, theta, phi, n_qubits).dot(state)
# Check that the state obtained using the circuit is a ground state
difference = sparse_operator * state - ground_energy * state
discrepancy = numpy.amax(numpy.abs(difference))
self.assertAlmostEqual(discrepancy, 0)
def test_excited_state_particle_nonconserving(self):
"""Test getting an excited state of a Hamiltonian that conserves
particle number."""
for n_qubits in self.n_qubits_range:
# Initialize a non-particle-number-conserving Hamiltonian
quadratic_hamiltonian = random_quadratic_hamiltonian(
n_qubits, False)
# Pick some orbitals to occupy
num_occupied_orbitals = numpy.random.randint(1, n_qubits + 1)
occupied_orbitals = numpy.random.choice(range(n_qubits),
num_occupied_orbitals,
False)
# Compute the Gaussian state
circuit_energy, gaussian_state = jw_get_gaussian_state(
quadratic_hamiltonian, occupied_orbitals)
# Compute the true energy
orbital_energies, constant = (
quadratic_hamiltonian.orbital_energies())
energy = numpy.sum(orbital_energies[occupied_orbitals]) + constant
# Check that the energies match
self.assertAlmostEqual(energy, circuit_energy)
# Check that the state obtained using the circuit is an eigenstate
# with the correct eigenvalue
sparse_operator = get_sparse_operator(quadratic_hamiltonian)
difference = (sparse_operator * gaussian_state -
energy * gaussian_state)
discrepancy = numpy.amax(numpy.abs(difference))
self.assertAlmostEqual(discrepancy, 0)
def test_particle_conserving(self):
for n_qubits in self.n_qubits_range:
# Initialize a particle-number-conserving Hamiltonian
quadratic_hamiltonian = random_quadratic_hamiltonian(
n_qubits, True)
sparse_operator = get_sparse_operator(quadratic_hamiltonian)
# Diagonalize the Hamiltonian using the circuit
circuit_description = reversed(
quadratic_hamiltonian.diagonalizing_circuit())
for parallel_ops in circuit_description:
for op in parallel_ops:
i, j, theta, phi = op
gate = jw_sparse_givens_rotation(i, j, theta, phi,
n_qubits)
sparse_operator = (
gate.getH().dot(sparse_operator).dot(gate))
# Check that the result is diagonal
diag = scipy.sparse.diags(sparse_operator.diagonal())
difference = sparse_operator - diag
discrepancy = 0.
if difference.nnz:
discrepancy = max(abs(difference.data))
numpy.testing.assert_allclose(discrepancy, 0.0, atol=1e-7)
# Check that the eigenvalues are in the expected order
orbital_energies, constant = (
quadratic_hamiltonian.orbital_energies())
for index in range(2**n_qubits):
bitstring = bin(index)[2:].zfill(n_qubits)
subset = [j for j in range(n_qubits) if bitstring[j] == '1']
energy = sum([orbital_energies[j] for j in subset]) + constant
self.assertAlmostEqual(sparse_operator[index, index], energy)
def test_not_implemented_spinr_reduced():
"""Tests that currently un-implemented functionality is caught."""
msg = "Specifying spin sector for non-particle-conserving "
msg += "Hamiltonians is not yet supported."
for n_qubits in [2, 4, 6]:
# Initialize a particle-number-conserving Hamiltonian
quadratic_hamiltonian = random_quadratic_hamiltonian(
n_qubits, False, True)
# Obtain the circuit
with pytest.raises(NotImplementedError):
_ = gaussian_state_preparation_circuit(quadratic_hamiltonian,
spin_sector=1)
def test_fqe_givens():
"""Test Givens Rotation evolution for correctness."""
# set up
norbs = 4
n_elec = norbs
sz = 0
n_qubits = 2 * norbs
time = 0.126
fqe_wfn = fqe.Wavefunction([[n_elec, sz, norbs]])
fqe_wfn.set_wfn(strategy="random")
ikappa = random_quadratic_hamiltonian(
norbs,
conserves_particle_number=True,
real=False,
expand_spin=False,
seed=2,
)
fqe_ham = RestrictedHamiltonian((ikappa.n_body_tensors[1, 0], ))
u = expm(-1j * ikappa.n_body_tensors[1, 0] * time)
# time-evolve
final_fqe_wfn = fqe_wfn.time_evolve(time, fqe_ham)
spin_ham = np.kron(ikappa.n_body_tensors[1, 0], np.eye(2))
assert of.is_hermitian(spin_ham)
ikappa_spin = of.InteractionOperator(
constant=0,
one_body_tensor=spin_ham,
two_body_tensor=np.zeros((n_qubits, n_qubits, n_qubits, n_qubits)),
)
bigU = expm(-1j * of.get_sparse_operator(ikappa_spin).toarray() * time)
initial_wf = fqe.to_cirq(fqe_wfn).reshape((-1, 1))
final_wf = bigU @ initial_wf
final_wfn_test = fqe.from_cirq(final_wf.flatten(), 1.0e-12)
assert np.allclose(final_fqe_wfn.rdm("i^ j"), final_wfn_test.rdm("i^ j"))
assert np.allclose(final_fqe_wfn.rdm("i^ j^ k l"),
final_wfn_test.rdm("i^ j^ k l"))
final_wfn_test2 = fqe.from_cirq(
evolve_wf_givens(initial_wf.copy(), u.copy()).flatten(), 1.0e-12)
givens_fqe_wfn = evolve_fqe_givens(fqe_wfn, u.copy())
assert np.allclose(givens_fqe_wfn.rdm("i^ j"), final_wfn_test2.rdm("i^ j"))
assert np.allclose(givens_fqe_wfn.rdm("i^ j^ k l"),
final_wfn_test2.rdm("i^ j^ k l"))
def test_ground_state_particle_nonconserving(self):
"""Test getting the ground state of a Hamiltonian that does not
conserve particle number."""
for n_qubits in self.n_qubits_range:
# Initialize a non-particle-number-conserving Hamiltonian
quadratic_hamiltonian = random_quadratic_hamiltonian(
n_qubits, False)
# Compute the true ground state
sparse_operator = get_sparse_operator(quadratic_hamiltonian)
ground_energy, _ = get_ground_state(sparse_operator)
# Compute the ground state using the circuit
circuit_energy, circuit_state = (
jw_get_gaussian_state(quadratic_hamiltonian))
# Check that the energies match
self.assertAlmostEqual(ground_energy, circuit_energy)
# Check that the state obtained using the circuit is a ground state
difference = (sparse_operator * circuit_state -
ground_energy * circuit_state)
discrepancy = numpy.amax(numpy.abs(difference))
self.assertAlmostEqual(discrepancy, 0)
def test_diagonalizing_bogoliubov_transform_particle_conserving(self):
"""Test particle-conserving diagonalizing Bogoliubov transform."""
# Spin-symmetric
quad_ham = random_quadratic_hamiltonian(5,
conserves_particle_number=True,
expand_spin=True)
quad_ham = get_quadratic_hamiltonian(
reorder(get_fermion_operator(quad_ham), up_then_down))
orbital_energies, transformation_matrix, _ = (
quad_ham.diagonalizing_bogoliubov_transform())
max_upper_right = numpy.max(numpy.abs(transformation_matrix[:5, 5:]))
max_lower_left = numpy.max(numpy.abs(transformation_matrix[5:, :5]))
numpy.testing.assert_allclose(orbital_energies[:5],
orbital_energies[5:])
numpy.testing.assert_allclose(transformation_matrix.dot(
quad_ham.combined_hermitian_part.T.dot(
transformation_matrix.T.conj())),
numpy.diag(orbital_energies),
atol=1e-7)
numpy.testing.assert_allclose(max_upper_right, 0.0)
numpy.testing.assert_allclose(max_lower_left, 0.0)
# Specific spin sector
quad_ham = random_quadratic_hamiltonian(5,
conserves_particle_number=True,
expand_spin=True)
quad_ham = get_quadratic_hamiltonian(
reorder(get_fermion_operator(quad_ham), up_then_down))
for spin_sector in range(2):
orbital_energies, transformation_matrix, _ = (
quad_ham.diagonalizing_bogoliubov_transform(
spin_sector=spin_sector))
def index_map(i):
return i + spin_sector * 5
spin_indices = [index_map(i) for i in range(5)]
spin_matrix = quad_ham.combined_hermitian_part[numpy.ix_(
spin_indices, spin_indices)]
numpy.testing.assert_allclose(transformation_matrix.dot(
spin_matrix.T.dot(transformation_matrix.T.conj())),
numpy.diag(orbital_energies),
atol=1e-7)
# Not spin-symmetric
quad_ham = random_quadratic_hamiltonian(5,
conserves_particle_number=True,
expand_spin=False)
orbital_energies, _ = quad_ham.orbital_energies()
_, transformation_matrix, _ = (
quad_ham.diagonalizing_bogoliubov_transform())
numpy.testing.assert_allclose(transformation_matrix.dot(
quad_ham.combined_hermitian_part.T.dot(
transformation_matrix.T.conj())),
numpy.diag(orbital_energies),
atol=1e-7)
def test_main_procedure(self):
for n in self.test_dimensions:
# Obtain a random quadratic Hamiltonian
quadratic_hamiltonian = random_quadratic_hamiltonian(n)
# Get the diagonalizing transformation
_, transformation_matrix, _ = (
quadratic_hamiltonian.diagonalizing_bogoliubov_transform())
left_block = transformation_matrix[:, :n]
right_block = transformation_matrix[:, n:]
lower_unitary = numpy.empty((n, 2 * n), dtype=complex)
lower_unitary[:, :n] = numpy.conjugate(right_block)
lower_unitary[:, n:] = numpy.conjugate(left_block)
# Get fermionic Gaussian decomposition of lower_unitary
decomposition, left_decomposition, diagonal, left_diagonal = (
fermionic_gaussian_decomposition(lower_unitary))
# Compute left_unitary
left_unitary = numpy.eye(n, dtype=complex)
for parallel_set in left_decomposition:
combined_op = numpy.eye(n, dtype=complex)
for op in reversed(parallel_set):
i, j, theta, phi = op
c = numpy.cos(theta)
s = numpy.sin(theta)
phase = numpy.exp(1.j * phi)
givens_rotation = numpy.array(
[[c, -phase * s], [s, phase * c]], dtype=complex)
givens_rotate(combined_op, givens_rotation, i, j)
left_unitary = combined_op.dot(left_unitary)
for i in range(n):
left_unitary[i] *= left_diagonal[i]
left_unitary = left_unitary.T
for i in range(n):
left_unitary[i] *= diagonal[i]
# Check that left_unitary zeroes out the correct entries of
# lower_unitary
product = left_unitary.dot(lower_unitary)
for i in range(n - 1):
for j in range(n - 1 - i):
self.assertAlmostEqual(product[i, j], 0.)
# Compute right_unitary
right_unitary = numpy.eye(2 * n, dtype=complex)
for parallel_set in decomposition:
combined_op = numpy.eye(2 * n, dtype=complex)
for op in reversed(parallel_set):
if op == 'pht':
swap_rows(combined_op, n - 1, 2 * n - 1)
else:
i, j, theta, phi = op
c = numpy.cos(theta)
s = numpy.sin(theta)
phase = numpy.exp(1.j * phi)
givens_rotation = numpy.array(
[[c, -phase * s], [s, phase * c]], dtype=complex)
double_givens_rotate(combined_op, givens_rotation, i,
j)
right_unitary = combined_op.dot(right_unitary)
# Compute left_unitary * lower_unitary * right_unitary^\dagger
product = left_unitary.dot(
lower_unitary.dot(right_unitary.T.conj()))
# Construct the diagonal matrix
diag = numpy.zeros((n, 2 * n), dtype=complex)
diag[range(n), range(n, 2 * n)] = diagonal
# Assert that W and D are the same
for i in numpy.ndindex((n, 2 * n)):
self.assertAlmostEqual(diag[i], product[i])
