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Multi Digit Ising Mapping for Low Precision Ising Solvers

Abhishek Kumar Singh, Kyle Jamieson

TL;DR

The paper addresses the precision gap in hardware Ising solvers by introducing a Multi-digit Ising mapping that artificially increases effective precision without hardware changes. It formalizes base-$q$ digit encoding (including 2-digit and 3-digit variants) to represent problem coefficients, introducing spin copies and penalty terms to realize higher precision while keeping coefficient ranges manageable. The approach is instantiated for DI-MIMO on a COBI Ising solver, achieving notable BER improvements in small MIMO configurations with 16-QAM under no-noise conditions. This technique broadens the practical impact of low-precision Ising hardware for hard problems like MIMO detection by bridging the gap between software-predicted gains and hardware realizations.

Abstract

The last couple of years have seen an ever-increasing interest in using different Ising solvers, like Quantum annealers, Coherent Ising machines, and Oscillator-based Ising machines, for solving tough computational problems in various domains. Although the simulations predict massive performance improvements for several tough computational problems, the real implementations of the Ising solvers tend to have limited precision, which can cause significant performance deterioration. This paper presents a novel methodology for mapping the problem on the Ising solvers to artificially increase the effective precision. We further evaluate our method for the Multiple-Input-Multiple-Output signal detection problem.

Multi Digit Ising Mapping for Low Precision Ising Solvers

TL;DR

The paper addresses the precision gap in hardware Ising solvers by introducing a Multi-digit Ising mapping that artificially increases effective precision without hardware changes. It formalizes base- digit encoding (including 2-digit and 3-digit variants) to represent problem coefficients, introducing spin copies and penalty terms to realize higher precision while keeping coefficient ranges manageable. The approach is instantiated for DI-MIMO on a COBI Ising solver, achieving notable BER improvements in small MIMO configurations with 16-QAM under no-noise conditions. This technique broadens the practical impact of low-precision Ising hardware for hard problems like MIMO detection by bridging the gap between software-predicted gains and hardware realizations.

Abstract

The last couple of years have seen an ever-increasing interest in using different Ising solvers, like Quantum annealers, Coherent Ising machines, and Oscillator-based Ising machines, for solving tough computational problems in various domains. Although the simulations predict massive performance improvements for several tough computational problems, the real implementations of the Ising solvers tend to have limited precision, which can cause significant performance deterioration. This paper presents a novel methodology for mapping the problem on the Ising solvers to artificially increase the effective precision. We further evaluate our method for the Multiple-Input-Multiple-Output signal detection problem.
Paper Structure (9 sections, 16 equations, 2 figures)

This paper contains 9 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Primer
  3. Ising Optimization
  4. MIMO Detection problem
  5. Design
  6. 2-digit simplification
  7. Evaluation
  8. COBI Ising solver
  9. Bit Error Rate Performance

Figures (2)

  • Figure 1: Bit error rate performance of native mapping vs 3-digit base-8 mapping for a $N_t=2$, $N_r =2$ MIMO system with 16-QAM modulation and no noise. We see that the proposed mapping can significantly improve the BER performance.
  • Figure 2: Bit error rate performance of native mapping vs 2-digit base-8 mapping for a $N_t=3$, $N_r =3$ MIMO system with 16-QAM modulation and no noise. We see that the proposed mapping can significantly improve the BER performance.