A Parallel Tempering Processing Architecture with Multi-Spin Update for Fully-Connected Ising Models

Combinatorial optimization problems (COPs) are notoriously difficult to solve for classic Von-Neumann computers, which are ubiquitous in various domains. As a state-of-the-art hardware acceleration scheme for COPs, Ising machines are one of the promising research directions for the next generation of computing, but still suffer from the low solution accuracy and speed due to the high complexity of the fully-connected Ising model. In this work, a novel parallel tempering processing architecture (PTPA) is proposed with the modified parallel tempering algorithm, aimed at reducing search time and improving the solution quality. Several techniques are developed to further reduce hardware overhead and enhance parallelism, including the independent pipelined spin update architecture, approximated probability equations, and compact random number generators. Its prototype is implemented on FPGA with eight replicas, each replica containing 1,024 fully-connected spins and at most 64 concurrent update spins. The proposed design achieves an average cut accuracy of 99.43% within 1ms solution time on various G-set problems. Compared with the CPU-based parallel tempering implementation, it enhances the speed of solving the max-cut problems by 5,160 times.

I. Introduction

Combinatorial optimization problems (COPs) can be found in various fields such as economic management, machine learning and communication network. Due to the fact that most of them are non-deterministic polynomial time hardness (NP-hard) problems [1], the corresponding solution space will increase exponentially as the problem size grows. Therefore, these problems are notoriously difficult for modern Von-Neumann computers when a brute-force search method is used [2].