Terastate-per-second QUBO Brute-Force on a Single GPU: A Matrix Prefix-Suffix Decomposition

Abstract

This paper presents a parallel QUBO exhaustive search algorithm for dense matrices, based on a prefix-suffix decomposition and Gray code ordering. The algorithm achieves O(1) per-state complexity: for the QUBO objective function computation only one arithmetic operation per state is performed. An adjustable energy components cache size enables placement in the fastest available memory tier. This reduces memory bandwidth requirements to a negligible level and transforms the problem from memory-bound to compute-bound. Our CUDA-based implementation achieves a state-of-the-art evaluation rate of $7.5\times10^{12}$ states per second on a single GPU, setting a new performance benchmark for the full-space-search subclass of exact solvers.