Permutation matrix representation quantum Monte Carlo
Abstract
We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its off-diagonal terms and is both parameter-free and Trotter error-free. In our approach, the quantum dimension consists of products of elements of a permutation group. As such, it allows for the study of a very wide variety of models on an equal footing. To demonstrate the utility of our technique, we use it to clarify the emergence of the sign problem in the simulations of non-stoquastic physical models. We showcase the flexibility of our algorithm and the advantages it offers over existing state-of-the-art by simulating transverse-field Ising model Hamiltonians and comparing the performance of our technique against that of the stochastic series expansion algorithm. We also study a transverse-field Ising model augmented with randomly chosen two-body transverse-field interactions.
- Authors:
-
- University of Southern California, Los Angeles, CA (United States)
- University of New Mexico, Albuquerque, NM (United States)
- University of Southern California, Los Angeles, CA (United States); University of Southern California, Marina del Rey, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of Southern California, Los Angeles, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Army Research Office (ARO)
- OSTI Identifier:
- 1656954
- Alternate Identifier(s):
- OSTI ID: 1830800
- Grant/Contract Number:
- SC0020280; W911NF-17-C-0050
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Statistical Mechanics
- Additional Journal Information:
- Journal Volume: 2020; Journal Issue: 7; Journal ID: ISSN 1742-5468
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Gupta, Lalit, Albash, Tameem, and Hen, Itay. Permutation matrix representation quantum Monte Carlo. United States: N. p., 2020.
Web. doi:10.1088/1742-5468/ab9e64.
Gupta, Lalit, Albash, Tameem, & Hen, Itay. Permutation matrix representation quantum Monte Carlo. United States. https://doi.org/10.1088/1742-5468/ab9e64
Gupta, Lalit, Albash, Tameem, and Hen, Itay. Tue .
"Permutation matrix representation quantum Monte Carlo". United States. https://doi.org/10.1088/1742-5468/ab9e64. https://www.osti.gov/servlets/purl/1656954.
@article{osti_1656954,
title = {Permutation matrix representation quantum Monte Carlo},
author = {Gupta, Lalit and Albash, Tameem and Hen, Itay},
abstractNote = {We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its off-diagonal terms and is both parameter-free and Trotter error-free. In our approach, the quantum dimension consists of products of elements of a permutation group. As such, it allows for the study of a very wide variety of models on an equal footing. To demonstrate the utility of our technique, we use it to clarify the emergence of the sign problem in the simulations of non-stoquastic physical models. We showcase the flexibility of our algorithm and the advantages it offers over existing state-of-the-art by simulating transverse-field Ising model Hamiltonians and comparing the performance of our technique against that of the stochastic series expansion algorithm. We also study a transverse-field Ising model augmented with randomly chosen two-body transverse-field interactions.},
doi = {10.1088/1742-5468/ab9e64},
journal = {Journal of Statistical Mechanics},
number = 7,
volume = 2020,
place = {United States},
year = {Tue Jul 28 00:00:00 EDT 2020},
month = {Tue Jul 28 00:00:00 EDT 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 3 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
On the computational complexity of curing non-stoquastic Hamiltonians
journal, April 2019
- Marvian, Milad; Lidar, Daniel A.; Hen, Itay
- Nature Communications, Vol. 10, Issue 1
Simulated Quantum Computation of Molecular Energies
journal, September 2005
- Aspuru-Guzik, A.
- Science, Vol. 309, Issue 5741
Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem
journal, January 2020
- Gupta, Lalit; Hen, Itay
- Advanced Quantum Technologies, Vol. 3, Issue 1
Quantum speedup at zero temperature via coherent catalysis
journal, March 2019
- Durkin, Gabriel A.
- Physical Review A, Vol. 99, Issue 3
Boson localization and the superfluid-insulator transition
journal, July 1989
- Fisher, Matthew P. A.; Weichman, Peter B.; Grinstein, G.
- Physical Review B, Vol. 40, Issue 1
Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stoquastic Hamiltonians
journal, February 2017
- Nishimori, Hidetoshi; Takada, Kabuki
- Frontiers in ICT, Vol. 4
Calculating the divided differences of the exponential function by addition and removal of inputs
journal, September 2020
- Gupta, Lalit; Barash, Lev; Hen, Itay
- Computer Physics Communications, Vol. 254
Role of nonstoquastic catalysts in quantum adiabatic optimization
journal, April 2019
- Albash, Tameem
- Physical Review A, Vol. 99, Issue 4
The complexity of stoquastic local Hamiltonian problems
journal, May 2008
- Bravyi, S.; DiVincenzo, D. P.; Oliveira, R.
- Quantum Information and Computation, Vol. 8, Issue 5
A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model
journal, July 1992
- Sandvik, A. W.
- Journal of Physics A: Mathematical and General, Vol. 25, Issue 13
Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems
journal, August 1998
- Prokof’ev, N. V.; Svistunov, B. V.; Tupitsyn, I. S.
- Journal of Experimental and Theoretical Physics, Vol. 87, Issue 2
The Monte Carlo method in quantum statistical mechanics
journal, October 1962
- Handscomb, D. C.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 58, Issue 4
Exchange Monte Carlo Method and Application to Spin Glass Simulations
journal, June 1996
- Hukushima, Koji; Nemoto, Koji
- Journal of the Physical Society of Japan, Vol. 65, Issue 6
Monte Carlo simulations with indefinite and complex-valued measures
journal, May 1994
- Kieu, T. D.; Griffin, C. J.
- Physical Review E, Vol. 49, Issue 5
Polynomial-time quantum algorithm for the simulation of chemical dynamics
journal, November 2008
- Kassal, I.; Jordan, S. P.; Love, P. J.
- Proceedings of the National Academy of Sciences, Vol. 105, Issue 48
A Monte Carlo method applied to the Heisenberg ferromagnet
journal, January 1964
- Handscomb, D. C.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 60, Issue 1
Quantum Monte Carlo annealing with multi-spin dynamics
journal, May 2017
- Mazzola, Guglielmo; Troyer, Matthias
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 5
From hypernuclei to the Inner Core of Neutron Stars: A Quantum Monte Carlo Study
journal, August 2014
- Lonardoni, D.; Pederiva, F.; Gandolfi, S.
- Journal of Physics: Conference Series, Vol. 529
Resolution of the sign problem for a frustrated triplet of spins
journal, March 2019
- Hen, Itay
- Physical Review E, Vol. 99, Issue 3
A quantum‐statistical Monte Carlo method; path integrals with boundary conditions
journal, March 1979
- Barker, J. A.
- The Journal of Chemical Physics, Vol. 70, Issue 6
Bose–Einstein condensation in magnetic insulators
journal, March 2008
- Giamarchi, Thierry; Rüegg, Christian; Tchernyshyov, Oleg
- Nature Physics, Vol. 4, Issue 3
Towards quantum chemistry on a quantum computer
journal, January 2010
- Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G.
- Nature Chemistry, Vol. 2, Issue 2
The cold atom Hubbard toolbox
journal, January 2005
- Jaksch, D.; Zoller, P.
- Annals of Physics, Vol. 315, Issue 1