Ising-machine-like Driving Condition Restrictions in SSBM and Additional Pseudo-annealing- Driving Method for SSBM that Achieves Best Cut Value Search -
Abstract
In our previous work, we proposed and experimentally demonstrated a physics-based simulator for combinatorial optimization problems (SSBM), which exploits a distinctive spontaneous symmetry breaking (SSB) phenomenon identified in a dissipative system exhibiting robust causality described by an iterative equation. We further conducted numerical simulations in which initial fluctuations of distinct patterns were applied to large-scale benchmark problems, and reported that the SSBM exhibits a unique behavior absent in conventional Ising machines: under specific conditions, pseudo-spin patterns progressively converge during the solution-search process and ultimately coalesce into a single pattern, with the cut value of the converged solution reaching 99.7% of the best-known cut value. In the present paper, we elucidate the conditions under which the SSBM can be configured to emulate the behavior of a continuous-variable Ising machine. We further demonstrate that by additionally incorporating an effect analogous to physical annealing into these conditions, the SSBM becomes capable of identifying the best-known cut value for the K_2000 benchmark instance.
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BibTeX
@misc{sato2026isingmachinelike,
title = {{Ising-machine-like Driving Condition Restrictions in SSBM and Additional Pseudo-annealing- Driving Method for SSBM that Achieves Best Cut Value Search -}},
author = {Toshiya Sato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.12545},
eprint = {2608.12545},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.12545},
}
RIS
TY - UNPB
TI - Ising-machine-like Driving Condition Restrictions in SSBM and Additional Pseudo-annealing- Driving Method for SSBM that Achieves Best Cut Value Search -
AU - Toshiya Sato
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2608.12545
UR - https://arxiv.org/abs/2608.12545
AB - In our previous work, we proposed and experimentally demonstrated a physics-based simulator for combinatorial optimization problems (SSBM), which exploits a distinctive spontaneous symmetry breaking (SSB) phenomenon identified in a dissipative system exhibiting robust causality described by an iterative equation. We further conducted numerical simulations in which initial fluctuations of distinct patterns were applied to large-scale benchmark problems, and reported that the SSBM exhibits a unique behavior absent in conventional Ising machines: under specific conditions, pseudo-spin patterns progressively converge during the solution-search process and ultimately coalesce into a single pattern, with the cut value of the converged solution reaching 99.7% of the best-known cut value. In the present paper, we elucidate the conditions under which the SSBM can be configured to emulate the behavior of a continuous-variable Ising machine. We further demonstrate that by additionally incorporating an effect analogous to physical annealing into these conditions, the SSBM becomes capable of identifying the best-known cut value for the K_2000 benchmark instance.
ER -