Inference from matrix products: a heuristic spin glass algorithm

Journal Article · Tue Jan 01 00:00:00 EST 2008 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.101.167206· OSTI ID:957795

Hastings, Matthew B ^[1]

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1. Los Alamos National Laboratory

We present an algorithm for finding ground states of two-dimensional spin-glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximation to the energy whose accuracy depends on a parameter k. We test the algorithm against exact methods on random field and random bond Ising models, and we find that accurate results require a k which scales roughly polynomially with the system size. The algorithm also performs well when tested on small systems with arbitrary interactions, where no fast, exact algorithms exist. The time required is significantly less than Monte Carlo schemes.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 957795
• Report Number(s): LA-UR-08-04666; LA-UR-08-4666; PRLTAO; TRN: US201016%%193
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ALGORITHMS
APPROXIMATIONS
GLASS
GROUND STATES
ISING MODEL
QUANTUM INFORMATION
SPIN