# A pure-sampling quantum Monte Carlo algorithm

## Abstract

The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static α polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and amore »

- Authors:

- Departments of Chemistry and Physics, Brock University, St. Catharines, Ontario L2S 3A1 (Canada)

- Publication Date:

- OSTI Identifier:
- 22415824

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; DIPOLE MOMENTS; ELECTRONS; EXPECTATION VALUE; EXTRAPOLATION; GROUND STATES; LITHIUM HYDRIDES; MOLECULES; MONTE CARLO METHOD; POLARIZABILITY; WATER; WAVE FUNCTIONS

### Citation Formats

```
Ospadov, Egor, and Rothstein, Stuart M., E-mail: srothstein@brocku.ca.
```*A pure-sampling quantum Monte Carlo algorithm*. United States: N. p., 2015.
Web. doi:10.1063/1.4905664.

```
Ospadov, Egor, & Rothstein, Stuart M., E-mail: srothstein@brocku.ca.
```*A pure-sampling quantum Monte Carlo algorithm*. United States. doi:10.1063/1.4905664.

```
Ospadov, Egor, and Rothstein, Stuart M., E-mail: srothstein@brocku.ca. Wed .
"A pure-sampling quantum Monte Carlo algorithm". United States.
doi:10.1063/1.4905664.
```

```
@article{osti_22415824,
```

title = {A pure-sampling quantum Monte Carlo algorithm},

author = {Ospadov, Egor and Rothstein, Stuart M., E-mail: srothstein@brocku.ca},

abstractNote = {The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static α polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and a variety of other properties for those systems.},

doi = {10.1063/1.4905664},

journal = {Journal of Chemical Physics},

number = 2,

volume = 142,

place = {United States},

year = {Wed Jan 14 00:00:00 EST 2015},

month = {Wed Jan 14 00:00:00 EST 2015}

}