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Title: Permutation matrix representation quantum Monte Carlo

Journal Article · · Journal of Statistical Mechanics
 [1];  [2];  [3]
  1. University of Southern California, Los Angeles, CA (United States)
  2. University of New Mexico, Albuquerque, NM (United States)
  3. University of Southern California, Los Angeles, CA (United States); University of Southern California, Marina del Rey, CA (United States)

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.

Research Organization:
Univ. of Southern California, Los Angeles, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Army Research Office (ARO)
Grant/Contract Number:
SC0020280; W911NF-17-C-0050
OSTI ID:
1656954
Alternate ID(s):
OSTI ID: 1830800
Journal Information:
Journal of Statistical Mechanics, Vol. 2020, Issue 7; ISSN 1742-5468
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

References (18)

On the computational complexity of curing non-stoquastic Hamiltonians journal April 2019
Simulated Quantum Computation of Molecular Energies journal September 2005
Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem journal January 2020
Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stoquastic Hamiltonians journal February 2017
Calculating the divided differences of the exponential function by addition and removal of inputs journal September 2020
A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model journal July 1992
Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems journal August 1998
The Monte Carlo method in quantum statistical mechanics journal October 1962
Polynomial-time quantum algorithm for the simulation of chemical dynamics journal November 2008
A Monte Carlo method applied to the Heisenberg ferromagnet journal January 1964
A Guide to Monte Carlo Simulations in Statistical Physics book January 2009
Quantum Monte Carlo annealing with multi-spin dynamics journal May 2017
Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs journal November 2012
From hypernuclei to the Inner Core of Neutron Stars: A Quantum Monte Carlo Study journal August 2014
A quantum‐statistical Monte Carlo method; path integrals with boundary conditions journal March 1979
Bose–Einstein condensation in magnetic insulators journal March 2008
Towards quantum chemistry on a quantum computer journal January 2010
The cold atom Hubbard toolbox journal January 2005

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