Optimization in random field Ising models by quantum annealing

2005/11/30 by Matti Sarjala, Viljo Petäjä, Mikko Alava · 3 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn

paper · pdf · doi:10.1088/1742-5468/2006/01/p01008

published as J. Stat. Mech. (2006) P01008 · 7 pages (2 columns), 9 figures, published with minor changes, one reference updated after the publication

openalex publication_date 2006/01/16 · arxiv created 2006/01/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is found to be e res ∼ log( N MC ) − ζ with ζ in the range 2...6, depending on the strength of the random field. Systems with 'large clusters' are harder to optimize as measured by ζ. Our numerical results suggest that in the ordered phase ζ = 2 whereas in the paramagnetic phase the annealing procedure can be tuned so that ζ → 6.

Citations

• Quantum Annealing in the Transverse Ising Model
• Susceptibility and percolation in two-dimensional random field Ising magnets
• Three-dimensional random-field Ising magnet: Interfaces, scaling, and the nature of states

Cited by

• Colloquium: Quantum annealing and analog quantum computation
• Convergence theorems for quantum annealing
• Low-energy excitations in the three-dimensional random-field Ising model