Requirements on bit resolution in optical Ising machine implementations

TL;DR

The paper addresses the impact of limited optical modulator bit-resolution on optical Ising machines (IMs) used for hard optimization. It employs numerical simulations of an analog IM with a digitized feedback term, and benchmarks performance on MaxCut problems from BiqMac and Gset to determine minimum required bit-resolution. The key finding is that 8-bit modulation is sufficient to reproduce float-feedback performance across tested problems, while 1-bit feedback can dramatically reduce time-to-solution (TTS) despite sometimes lower transient success rates. This suggests practical hardware benefits, including lower power and cost, with 1-bit feedback offering a substantial speedup and robustness across problem sizes.

Abstract

Optical Ising machines have emerged as a promising dynamical hardware solver for computational hard optimization problems. These Ising machines typically require an optical modulator to represent the analog spin variables of these problems. However, modern day optical modulators have a relatively low modulation resolution. We therefore investigate how the low bit-resolution of optical hardware influences the performance of this type of novel computing platform. Based on numerical simulations, we determine the minimum required bit-resolution of an optical Ising machine for different benchmark problems of different sizes. Our study shows that a limited bit-resolution of 8bit is sufficient for the optical modulator. Surprisingly, we also observe that the use of a 1bit-resolution modulator significantly improves the performance of the Ising machine across all considered benchmark problems.

Figures (5)

• Figure 1: Essential building blocks of an analog Ising machine, where the specific type of non-linearity depends on the hardware being used.
• Figure 2: (a) The spin evolution and (b) the energy evolution of the IM solving g05$\_$100.2 biqmac problem with float-feedback. The horizontal line in (b) indicates the known ground state energy of the benchmark problem. (c) Transient success rate of the g05$\_$100.2 biqmac problem, as a function of bit-resolution. The orange and black line indicate the average the transient success rate of the float- and bit feedback respectively. The standard deviation is indicated by the shaded areas around this average.
• Figure 3: (a) The required bit resolution for three different problem sets is evaluated, with each set consisting of 10 MaxCut problems. Each problem set has a different size (60, 80, and 100 spins) and is represented by a distinct color. The x-axis shows the problem numbers for each set. A horizontal dashed line at 8bit indicates the minimum required bit resolution for all the benchmark problems considered. (b) The required bit resolution for different problem sizes. For the network size uptill 300 spins, the Biqmac library is used, while for larger problem sizes the Gset library was used. The red triangle visualizes the average required bit-resolution for each problem size while te error bars obtained bit-resolution in each used data set.
• Figure 4: The average transient success rate and TTS as a function of runtime. (a)-(c) show how the average transient success rate changes with increasing runtime. The considered MaxCut problems are the 100.2, 100.4 and 100.9 respectively. All three problems are taken from the BiqMac library. (d)-(f) show how the average TTS changes with runtime. The problems considered are again 100.2, 100.4 and 100.9 respectively. The red arrowes inidacte the effective TTS and in all three cases, the 1bit feedback system has a smaller effective TTS than the float feedback system.
• Figure 5: (a) Spin evolution of the system with the an optimized bit feedback and (b) an optimized float feedback. The vertical blue (red) line indicates the time at which the GS is first reached for the 1bit feedback (float feedback). Pannel (c) shows the associated energy evolution of both feedback systems.