Label-Permutation Symmetry and Stability in Oscillator Potts Machines
Abstract
Oscillator Potts machines (OPMs) provide a physics-inspired, energy-minimization framework for solving combinatorial optimization problems described by the q-state Potts Hamiltonian. Although OPMs may be viewed as multistate extensions of oscillator Ising machines (OIMs), here, we show that they exhibit dynamical properties absent in the binary case. Specifically, we derive a configuration-dependent local-stability condition for a recently proposed multiharmonic OPM formulation and show that configurations with the same Potts energy need not be dynamically equivalent. In particular, for q≥4, permutations of the Potts labels can alter the Jacobian spectrum and, consequently, the regularization strength required to locally stabilize a given Potts configuration. Thus, different phase encodings of the same Potts solution can exhibit different local stability properties despite having identical Potts energies.
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BibTeX
@misc{ekanayake2026labelpermutation,
title = {{Label-Permutation Symmetry and Stability in Oscillator Potts Machines}},
author = {E. M. Hasantha Ekanayake and Nikhil Shukla},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36716},
eprint = {2609.36716},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36716},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Label-Permutation Symmetry and Stability in Oscillator Potts Machines
AU - E. M. Hasantha Ekanayake
AU - Nikhil Shukla
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36716
UR - https://arxiv.org/abs/2609.36716
AB - Oscillator Potts machines (OPMs) provide a physics-inspired, energy-minimization framework for solving combinatorial optimization problems described by the q-state Potts Hamiltonian. Although OPMs may be viewed as multistate extensions of oscillator Ising machines (OIMs), here, we show that they exhibit dynamical properties absent in the binary case. Specifically, we derive a configuration-dependent local-stability condition for a recently proposed multiharmonic OPM formulation and show that configurations with the same Potts energy need not be dynamically equivalent. In particular, for q≥4, permutations of the Potts labels can alter the Jacobian spectrum and, consequently, the regularization strength required to locally stabilize a given Potts configuration. Thus, different phase encodings of the same Potts solution can exhibit different local stability properties despite having identical Potts energies.
ER -