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Multi-Phase Coupled CMOS Ring Oscillator based Potts Machine

Yilmaz Ege Gonul, Baris Taskin

TL;DR

The paper addresses NP-hard COPs by extending oscillator-based Ising machines to the Potts framework, enabling multivalued spins with a CMOS ring-oscillator network. It introduces the ROPM, where each oscillator supports N-phase spins via N-SHIL synchronization, enabling efficient encoding of problems like $3$-coloring. Through extensive simulations on DIMACS SATLIB benchmarks and larger random graphs, the ROPM achieves about 89–93% accuracy with linear power growth and scalable hardware in 65 nm CMOS, demonstrating practical viability for multivalued spin problems. This work offers a scalable, silicon-friendly approach to energy minimization in COPs, potentially enabling faster and more power-efficient solutions for complex graph-coloring and related tasks.

Abstract

This paper presents a coupled ring oscillator based Potts ma chine to solve NP-hard combinatorial optimization problems (COPs). Potts model is a generalization of the Ising model, cap turing multivalued spins in contrast to the binary-valued spins allowed in the Ising model. Similar to recent literature on Ising machines, the proposed architecture of Potts machines imple ments the Potts model with interacting spins represented by cou pled ring oscillators. Unlike Ising machines which are limited to two spin values, Potts machines model COPs that require a larger number of spin values. A major novelty of the proposed Potts machine is the utilization of the N-SHIL (Sub-Harmonic Injection Locking) mechanism, where multiple stable phases are obtained from a single (i.e. ring) oscillator. In evaluation, 3 coloring problems from the DIMACS SATBLIB benchmark and two randomly generated larger problems are mapped to the pro posed architecture. The proposed architecture is demonstrated to solve problems of varying size with 89% to 92% accuracy averaged over multiple iterations. The simulation results show that there is no degradation in accuracy, no significant increase in solution time, and only a linear increase in power dissipation with increasing problem sizes up to 2000 nodes.

Multi-Phase Coupled CMOS Ring Oscillator based Potts Machine

TL;DR

The paper addresses NP-hard COPs by extending oscillator-based Ising machines to the Potts framework, enabling multivalued spins with a CMOS ring-oscillator network. It introduces the ROPM, where each oscillator supports N-phase spins via N-SHIL synchronization, enabling efficient encoding of problems like -coloring. Through extensive simulations on DIMACS SATLIB benchmarks and larger random graphs, the ROPM achieves about 89–93% accuracy with linear power growth and scalable hardware in 65 nm CMOS, demonstrating practical viability for multivalued spin problems. This work offers a scalable, silicon-friendly approach to energy minimization in COPs, potentially enabling faster and more power-efficient solutions for complex graph-coloring and related tasks.

Abstract

This paper presents a coupled ring oscillator based Potts ma chine to solve NP-hard combinatorial optimization problems (COPs). Potts model is a generalization of the Ising model, cap turing multivalued spins in contrast to the binary-valued spins allowed in the Ising model. Similar to recent literature on Ising machines, the proposed architecture of Potts machines imple ments the Potts model with interacting spins represented by cou pled ring oscillators. Unlike Ising machines which are limited to two spin values, Potts machines model COPs that require a larger number of spin values. A major novelty of the proposed Potts machine is the utilization of the N-SHIL (Sub-Harmonic Injection Locking) mechanism, where multiple stable phases are obtained from a single (i.e. ring) oscillator. In evaluation, 3 coloring problems from the DIMACS SATBLIB benchmark and two randomly generated larger problems are mapped to the pro posed architecture. The proposed architecture is demonstrated to solve problems of varying size with 89% to 92% accuracy averaged over multiple iterations. The simulation results show that there is no degradation in accuracy, no significant increase in solution time, and only a linear increase in power dissipation with increasing problem sizes up to 2000 nodes.

Paper Structure

This paper contains 17 sections, 5 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background on ROSC based Ising Machines
  3. General Theory on Ising Model and Machines
  4. Review of ROSC based Ising Machines
  5. Coupled ROSC-based Potts Machine Design
  6. General Theory on Potts Model and Machines
  7. Review of Potts Machines in Literature vs the Proposed ROPM
  8. ROSCs for the Proposed ROPM
  9. N-SHIL for the Proposed ROPM
  10. Implementation of the Proposed ROPM
  11. Mapping 3-Coloring Problem to a Potts Machine
  12. Probabilistic Computation of Potts Machines
  13. Simulation Results
  14. Analysis of ROPM Performance Metrics
  15. Comparison of Results with Prior Work
  16. ...and 2 more sections

Figures (8)

  • Figure 1: a) Two ROSCs negatively coupled with an inverting coupling medium (B2B inverters) b) Coupled ROSC phases progressively locking out of phase through time
  • Figure 2: A 5-node graph 3-colored with a) an OIM limited to capturing 2 distinct spins with a single oscillator b) an OPM capable of capturing 3 distinct spins with a single oscillator
  • Figure 3: Illustrations of phase locking in the cases of perturbations by SHIL with a) the $1^{st}$ harmonic (fundamental) b) $2^{nd}$ harmonic c) $3^{rd}$ harmonic of the base frequency
  • Figure 4: 3-SHIL susceptibility analysis of the proposed ROSC sizing (a) PPV waveform from one the ROSC nodes b) Fourier transform of the PPV showing harmonic components
  • Figure 5: a) ROSC block with local and global enable signals (L_EN and G_EN) and SYNC (for N-SHIL) injected through a pass transistor b) Coupling block containing B2B inverters with local and global enables (L_EN and G_EN)
  • ...and 3 more figures