Re'class'ification of 'quant'ified classical simulated annealing

2008/10/03 by Toshiyuki Tanaka
Mathematics · Physics and Astronomy · #Geometry #Markov Chains and Monte Carlo Methods #Markov chain #Mathematics #Physics #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Reinterpretation #Scaling #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #physics.comp-ph

paper · pdf · doi:10.1088/1742-6596/143/1/012020

8 pages, 1 figure, presentation given at: International Workshop on Statistical-Mechanical Informatics 2008, Sendai, Japan

arxiv created 2008/10/03 · openalex publication_date 2009/01/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We discuss a classical reinterpretation of quantum-mechanics-based analysis of classical Markov chains with detailed balance, that is based on the quantum-classical correspondence. The classical reinterpretation is then used to demonstrate that it successfully reproduces a sufficient condition for cooling schedule in classical simulated annealing, which has the inverse-logarithmic scaling.

Citations

• From quantum mechanics to classical statistical physics: Generalized Rokhsar–Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition
• From classical to quantum dynamics at Rokhsar–Kivelson points
• Mathematical foundation of quantum annealing
• Quantum three-coloring dimer model and the disruptive effect of quantum glassiness on its line of critical points
• Criticality, the area law, and the computational power of PEPS