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)