Anechoic: Onsager-Corrected Parallel Annealing for Sub-0.1 ms Dense Max-Cut on an FPGA

Abstract

Ising machines solve combinatorial optimization problems by annealing a network of spins. On dense problems, the least expensive hardware step updates all spins at once: stochastic cellular automata (SCA) decide every spin in parallel and read couplings only for the spins that flip. Such synchronous updates create an echo: the previous state of each spin returns to it through its neighbors. On K2000, a Max-Cut benchmark on a 2,000-node complete graph, two-thirds of all flips undo the same spin's flip one step earlier. This paper presents Anechoic, an FPGA Ising machine that subtracts this echo from every decision. Dynamical mean-field theory identifies the echo as an Onsager reaction; its one-step strength is the number of spins whose flip probability is strictly between 0 and 1, divided by twice the temperature. The decision logic already flags these spins, so the correction costs one population count per step; a temperature-scaled form needs none. An RTL engine executes a dense 2,000-spin step in 18.1 cycles plus 0.14 per flip, so every saved step and flip saves time. Both forms find better K2000 cuts at every step budget than five published binary-spin algorithms at their papers' settings. Twelve engines at 250 MHz on an AMD Alveo V80 reach a cut of at least 33,000 with 99% probability in 0.05 ms, 5.2 times faster than the fastest published hardware, at 5.4 mJ per solution; with 2-bit couplings, the temperature-scaled form is also faster than uncorrected SCA on 49 of 51 G-set graphs. On an NVIDIA GH200 GPU, the same engine is 2.3 times slower and needs 8.0 times more energy per solution, though its 240 concurrent anneals give 2.3 times the throughput. As a GlobalFoundries 22 nm ASIC at 1.25 GHz, twelve engines would reach the target in about 10 microseconds, 26 times faster than the fastest published hardware. The code is available at https://github.com/skethz/anechoic.