Pushing the boundary of quantum advantage in hard combinatorial optimization with probabilistic computers.

Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet their advantage for real-world problems remains an open question. Here, we show that probabilistic computers, co-designed with hardware to implement Monte Carlo algorithms, provide a scalable classical pathway for solving hard optimization problems. We focus on two algorithms applied to three-dimensional spin glasses: discrete-time simulated quantum annealing and adaptive parallel tempering. We benchmark these methods against a leading quantum annealer. For simulated quantum annealing, increasing replicas improves residual energy scaling, consistent with extreme value theory. Adaptive parallel tempering, supported by non-local isoenergetic cluster moves, scales more favorably and outperforms simulated quantum annealing. Field Programmable Gate Arrays or specialized chips can implement these algorithms in modern hardware, leveraging massive parallelism to accelerate them while improving energy efficiency. Our results establish a rigorous classical baseline for assessing practical quantum advantage and present probabilistic computers as a scalable platform for real-world optimization challenges.