Probabilistic Computers for MIMO Detection: From Sparsification to 2D Parallel Tempering

Probabilistic computers built from p-bits offer a promising path for combinatorial optimization, but the dense connectivity required by real-world problems scales poorly in hardware. Here, we address this through graph sparsification with auxiliary copy variables and demonstrate a fully on-chip parallel tempering solver on an FPGA. Targeting MIMO detection, a dense, NP-hard problem central to wireless communications, we fit 15 temperature replicas of a 128-node sparsified system (1,920 p-bits) entirely on-chip and achieve bit error rates significantly below conventional linear detectors. We report complete end-to-end solution times of 4.7 ms per instance, with all loading, sampling, readout, and verification overheads included. ASIC projections in 7 nm technology indicate about 90 MHz operation with less than 200 mW power dissipation, suggesting that massive parallelism across multiple chips could approach the throughput demands of next-generation wireless systems. However, sparsification introduces sensitivity to the copy-constraint strength. Employing Two-Dimensional Parallel Tempering (2D-PT), which exchanges replicas across both temperature and constraint dimensions, we demonstrate over 10X faster convergence without manual parameter tuning. These results establish an on-chip p-bit architecture and a scalable algorithmic framework for dense combinatorial optimization.