Domain-specific hardware to solve computationally hard optimization problems has generated tremendous excitement recently. Here, we evaluate probabilistic bit (p-bit) based on Ising Machines (IM) or p-computers with a benchmark combinatorial optimization problem, namely the 3-regular 3-XOR Satisfiability (3R3X). The 3R3X problem has a glassy energy landscape, and it has recently been used to benchmark various IMs and other solvers. We introduce a multiplexed architecture where p-computers emulate all-to-all (complete) graph functionality despite being interconnected in sparse networks, enabling a highly parallelized chromatic Gibbs sampling. We implement this architecture in FPGAs and show that p-bit networks running an adaptive version of the powerful parallel tempering algorithm demonstrate competitive algorithmic and prefactor advantages over alternative IMs by D-Wave, Toshiba, and Fujitsu, except a greedy algorithm accelerated on a GPU. We further extend our APT results using higher-order interactions in FPGAs and show that while higher-order interactions lead to prefactor advantages, they do not show any algorithmic scaling advantages for the XORSAT problem, settling an open conjecture. Even though FPGA implementations of p-bits are still not quite as fast as the best possible greedy algorithms implemented in GPUs, scaled magnetic versions of p-computers could lead to orders of magnitude over such algorithms according to experimentally established projections.

翻译：用于求解计算困难优化问题的领域专用硬件近来引起了极大关注。本文通过基准组合优化问题——三正则三异或可满足性（3R3X），对基于伊辛机（IM）或概率比特计算机（p-计算机）的概率比特（p-bit）进行评估。3R3X问题具有玻璃态能量景观，近期已被用于基准测试各类伊辛机及其他求解器。我们提出一种多路复用架构，使得在稀疏网络中互连的p-计算机能够模拟全连接（完全图）功能，从而实现高度并行的色度吉布斯采样。我们在FPGA中实现该架构，并证明运行自适应并行回火算法的p-bit网络相较于D-Wave、东芝和富士通的替代伊辛机具有竞争优势的算法优势与前置因子优势（GPU加速的贪婪算法除外）。我们进一步利用FPGA中的高阶相互作用扩展自适应并行回火算法研究，结果表明：虽然高阶相互作用能带来前置因子优势，但对于XORSAT问题并未显示出算法扩展优势，这解决了一个悬而未决的猜想。尽管p-bit的FPGA实现速度仍不及GPU最佳贪婪算法，但根据实验验证的预测，规模化磁性版本p-计算机可能较此类算法实现数量级的性能提升。