braket.experimental.algorithms.qc_qmc.classical_qmc module

class braket.experimental.algorithms.qc_qmc.classical_qmc.ChemicalProperties(h1e: numpy.ndarray, eri: numpy.ndarray, nuclear_repulsion: float, v_0: numpy.ndarray, h_chem: numpy.ndarray, v_gamma: List[numpy.ndarray], l_gamma: List[numpy.ndarray], mf_shift: numpy.ndarray, lambda_l: List[numpy.ndarray], u_l: List[numpy.ndarray])

Bases: object

h1e: ndarray

eri: ndarray

nuclear_repulsion: float

v_0: ndarray

h_chem: ndarray

v_gamma: List[ndarray]

l_gamma: List[ndarray]

mf_shift: ndarray

lambda_l: List[ndarray]

u_l: List[ndarray]

braket.experimental.algorithms.qc_qmc.classical_qmc.classical_qmc(num_walkers: int, num_steps: int, dtau: float, trial: ndarray, prop: ChemicalProperties, max_pool: int = 8) → Tuple[float, float]

Classical Auxiliary-Field Quantum Monte Carlo.

Parameters:

• num_walkers (int) – Number of walkers.

• num_steps (int) – Number of (imaginary) time steps

• dtau (float) – Increment of each time step

• trial (ndarray) – Trial wavefunction.

• prop (ChemicalProperties) – Chemical properties.

• max_pool (int) – Max workers. Defaults to 8.

Returns:

Tuple[float, float] – Energies

braket.experimental.algorithms.qc_qmc.classical_qmc.hartree_fock_energy(trial: ndarray, prop: ChemicalProperties) → float

Compute Hatree Fock energy.

Parameters:

• trial (ndarray) – Trial wavefunction.

• prop (ChemicalProperties) – Chemical properties.

Returns:

float – Energy

braket.experimental.algorithms.qc_qmc.classical_qmc.full_imag_time_evolution_wrapper(args: Tuple) → Callable

braket.experimental.algorithms.qc_qmc.classical_qmc.full_imag_time_evolution(num_steps: int, dtau: float, trial: ndarray, prop: ChemicalProperties, e_shift: float, walker: ndarray, weight: float) → Tuple[List[float], float]

Imaginary time evolution of a single walker.

Parameters:

• num_steps (int) – number of time steps

• dtau (float) – imaginary time step size

• trial (ndarray) – trial state as np.ndarray, e.g., for h2 HartreeFock state, it is np.array([[1,0], [0,1], [0,0], [0,0]])

• prop (ChemicalProperties) – Chemical properties.

• e_shift (float) – Reference energy, i.e. Hartree-Fock energy

• walker (ndarray) – normalized walker state as np.ndarray, others are the same as trial

• weight (float) – weight for sampling.

Returns:

Tuple[List[float], float] – energy_list, weights

braket.experimental.algorithms.qc_qmc.classical_qmc.imag_time_propogator(dtau: float, trial: ndarray, walker: ndarray, weight: float, prop: ChemicalProperties, e_shift: float) → Tuple[float, ndarray, float]

Propagate a walker by one time step.

Parameters:

• dtau (float) – imaginary time step size

• trial (ndarray) – trial state as np.ndarray, e.g., for h2 HartreeFock state, it is np.array([[1,0], [0,1], [0,0], [0,0]])

• walker (ndarray) – normalized walker state as np.ndarray, others are the same as trial

• weight (float) – weight for sampling.

• prop (ChemicalProperties) – Chemical properties.

• e_shift (float) – Reference energy, i.e. Hartree-Fock energy

Returns:

Tuple[float, ndarray, float] – e_loc, new_walker, new_weight

braket.experimental.algorithms.qc_qmc.classical_qmc.local_energy(h1e: ndarray, eri: ndarray, green_funcs: ndarray, enuc: float) → float

Calculate local energy for generic two-body Hamiltonian using the full (spatial) form for the two-electron integrals.

Parameters:

• h1e (ndarray) – one-body term.

• eri (ndarray) – two-body term.

• green_funcs (ndarray) – Walker’s “green’s function”.

• enuc (float) – Nuclear repulsion energy.

Returns:

float – kinetic, potential energies and nuclear repulsion energy.

braket.experimental.algorithms.qc_qmc.classical_qmc.reortho(A: ndarray) → Tuple[ndarray, float]

Reorthogonalise a MxN matrix A. Performs a QR decomposition of A. Note that for consistency elsewhere we want to preserve detR > 0 which is not guaranteed. We thus factor the signs of the diagonal of R into Q.

Parameters:

A (ndarray) – MxN matrix.

Returns:

Tuple[ndarray, float] – (Q, detR) Q (ndarray): Orthogonal matrix. A = QR. detR (float): Determinant of upper triangular matrix (R) from QR decomposition.

braket.experimental.algorithms.qc_qmc.classical_qmc.greens_pq(psi: ndarray, phi: ndarray) → ndarray

This function computes the one-body Green’s function.

Parameters:

• psi (ndarray) – wavefunction

• phi (ndarray) – wavefunction

Returns:

ndarray – one-body Green’s function

braket.experimental.algorithms.qc_qmc.classical_qmc.chemistry_preparation(mol: Molecule, geometry: ndarray, trial: ndarray) → ChemicalProperties

Return the one- and two-electron integrals from Pennylane.

Parameters:

• mol (Molecule) – Pennylane molecular structure.

• geometry (ndarray) – Atomic coordiantes for the molecule.

• trial (ndarray) – Trial wavefunction.

Returns:

ChemicalProperties – chemical properties v_0: one-body term stored as np.ndarray, with mean-field subtraction h_chem: one-body term stored as np.ndarray, without mean-field subtraction v_gamma: 1.j*l_gamma l_gamma: Cholesky vector decomposed from two-body terms mf_shift: mean-field shift nuclear_repulsion: nuclear repulsion constant

braket.experimental.algorithms.qc_qmc.classical_qmc.propagate_walker(x: ndarray, v_0: List[ndarray], v_gamma: List[ndarray], mf_shift: ndarray, dtau: float, trial: ndarray, walker: ndarray, green_funcs: List[ndarray]) → ndarray

Update the walker forward in imaginary time.

Parameters:

• x (ndarray) – auxiliary fields

• v_0 (List[ndarray]) – modified one-body term from reordering the two-body operator + mean-field subtraction.

• v_gamma (List[ndarray]) – Cholesky vectors stored in list (L, num_spin_orbitals, num_spin_orbitals), without mf_shift.

• mf_shift (ndarray) – mean-field shift Bar{v}_{gamma} stored in np.array format

• dtau (float) – imaginary time step size

• trial (ndarray) – trial state as np.ndarray, e.g., for h2 HartreeFock state, it is np.array([[1,0], [0,1], [0,0], [0,0]])

• walker (ndarray) – walker state as np.ndarray, others are the same as trial

• green_funcs (List[ndarray]) – one-body Green’s function

Returns:

ndarray – new walker for next time step