A fully parallel densely connected probabilistic Ising machine with inertia for real-time applications

TL;DR

This paper introduces a modified Ising machine with inertia that enables fully parallel updates, significantly increasing speed and maintaining solution quality for dense problems in real-time applications.

Contribution

It presents a novel inertia-based spin dynamics allowing fully parallel updates in probabilistic Ising machines, verified through simulations and FPGA hardware, enhancing speed for dense problem solving.

Findings

Achieved an average 35x speedup on Max-Cut and SK-1 models at 200 spins.

Demonstrated practical utility in real-time 5G MIMO detection with hardware co-design.

Enabled fully parallel updates without degrading success probability.

Abstract

Ising machines -- special-purpose hardware for heuristically solving Ising optimization problems -- based on probabilistic bits (p-bits) have been established as a promising alternative to heuristic optimization algorithms run on conventional computers. However, it has -- until now -- been thought that Ising spins that are connected in probabilistic Ising machines cannot be updated in parallel without ruining the machine's solving ability. This has been a major challenge for using probabilistic Ising machines as fast solvers for densely connected problems. Here, we circumvent this by introducing a modified Ising spin dynamics with an added inertia term, and verify in algorithm simulations, FPGA hardware emulation, and FPGA experiments that it enables fully parallel, synchronous updates while improving rather than degrading success probability. We evaluated on various types of abstract (Max-Cut and Sherrington-Kirkpatrick-model) and application-derived (MIMO, wireless detection) dense Ising benchmark instances. Performing fully parallel updates results in a speed advantage that grows faster than linearly with the number of spins, giving rise to large time-to-solution increases for practical problem sizes. For both Max-Cut and the SK-1 model at a problem size of 200, our approach achieved an average speedup of $\approx 35\times$, with the best single-instance speedup reaching $150\times$. As an example of the practical utility of our approach in an application where speed is critical, we further show by co-designing the algorithm dynamics with the hardware implementation -- co-optimizing for solver ability and silicon resource usage -- that probabilistic Ising machines based on our approach satisfy the stringent solution quality and latency/throughput requirements for real-time MIMO detection in modern 5G cellular wireless networks while using a practically reasonable silicon area.