def test_bogoliubov_transform_quadratic_hamiltonian_inverse_is_dagger(
n_qubits, real, particle_conserving, atol):
quad_ham = random_quadratic_hamiltonian(
n_qubits,
real=real,
conserves_particle_number=particle_conserving,
seed=46533)
_, transformation_matrix, _ = quad_ham.diagonalizing_bogoliubov_transform()
qubits = cirq.LineQubit.range(n_qubits)
if transformation_matrix.shape == (n_qubits, n_qubits):
daggered_transformation_matrix = transformation_matrix.T.conj()
else:
left_block = transformation_matrix[:, :n_qubits]
right_block = transformation_matrix[:, n_qubits:]
daggered_transformation_matrix = numpy.block(
[left_block.T.conj(), right_block.T])
circuit1 = cirq.Circuit(
cirq.inverse(bogoliubov_transform(qubits, transformation_matrix)))
circuit2 = cirq.Circuit(
bogoliubov_transform(qubits, daggered_transformation_matrix))
cirq.testing.assert_allclose_up_to_global_phase(circuit1.unitary(),
circuit2.unitary(),
atol=atol)
def test_bogoliubov_transform_quadratic_hamiltonian(n_qubits,
conserves_particle_number,
atol=5e-5):
qubits = LineQubit.range(n_qubits)
# Initialize a random quadratic Hamiltonian
quad_ham = random_quadratic_hamiltonian(n_qubits,
conserves_particle_number,
real=False)
quad_ham_sparse = get_sparse_operator(quad_ham)
# Compute the orbital energies and circuit
orbital_energies, constant = quad_ham.orbital_energies()
transformation_matrix = quad_ham.diagonalizing_bogoliubov_transform()
circuit = cirq.Circuit.from_ops(
bogoliubov_transform(qubits, transformation_matrix))
# Pick some random eigenstates to prepare, which correspond to random
# subsets of [0 ... n_qubits - 1]
n_eigenstates = min(2**n_qubits, 5)
subsets = [
numpy.random.choice(range(n_qubits),
numpy.random.randint(1, n_qubits + 1), False)
for _ in range(n_eigenstates)
]
# Also test empty subset
subsets += [()]
for occupied_orbitals in subsets:
# Compute the energy of this eigenstate
energy = (sum(orbital_energies[i]
for i in occupied_orbitals) + constant)
# Construct initial state
initial_state = sum(2**(n_qubits - 1 - int(i))
for i in occupied_orbitals)
# Get the state using a circuit simulation
state1 = circuit.apply_unitary_effect_to_state(initial_state)
# Also test the option to start with a computational basis state
special_circuit = cirq.Circuit.from_ops(
bogoliubov_transform(qubits,
transformation_matrix,
initial_state=initial_state))
state2 = special_circuit.apply_unitary_effect_to_state(
initial_state, qubits_that_should_be_present=qubits)
# Check that the result is an eigenstate with the correct eigenvalue
numpy.testing.assert_allclose(quad_ham_sparse.dot(state1),
energy * state1,
atol=atol)
numpy.testing.assert_allclose(quad_ham_sparse.dot(state2),
energy * state2,
atol=atol)
def test_spin_symmetric_bogoliubov_transform(
n_spatial_orbitals,
conserves_particle_number,
atol=5e-5):
n_qubits = 2*n_spatial_orbitals
qubits = LineQubit.range(n_qubits)
# Initialize a random quadratic Hamiltonian
quad_ham = random_quadratic_hamiltonian(
n_spatial_orbitals,
conserves_particle_number,
real=True,
expand_spin=True,
seed=28166)
# Reorder the Hamiltonian and get sparse matrix
quad_ham = openfermion.get_quadratic_hamiltonian(
openfermion.reorder(
openfermion.get_fermion_operator(quad_ham),
openfermion.up_then_down)
)
quad_ham_sparse = get_sparse_operator(quad_ham)
# Compute the orbital energies and transformation_matrix
up_orbital_energies, _, _ = (
quad_ham.diagonalizing_bogoliubov_transform(spin_sector=0))
down_orbital_energies, _, _ = (
quad_ham.diagonalizing_bogoliubov_transform(spin_sector=1))
_, transformation_matrix, _ = (
quad_ham.diagonalizing_bogoliubov_transform())
# Pick some orbitals to occupy
up_orbitals = list(range(2))
down_orbitals = [0, 2, 3]
energy = sum(up_orbital_energies[up_orbitals]) + sum(
down_orbital_energies[down_orbitals]) + quad_ham.constant
# Construct initial state
initial_state = (
sum(2**(n_qubits - 1 - int(i)) for i in up_orbitals)
+ sum(2**(n_qubits - 1 - int(i+n_spatial_orbitals))
for i in down_orbitals)
)
# Apply the circuit
circuit = cirq.Circuit.from_ops(
bogoliubov_transform(
qubits, transformation_matrix, initial_state=initial_state))
state = circuit.apply_unitary_effect_to_state(initial_state)
# Check that the result is an eigenstate with the correct eigenvalue
numpy.testing.assert_allclose(
quad_ham_sparse.dot(state), energy * state, atol=atol)