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

## TL;DR

Probabilistic computers, using Monte Carlo algorithms, offer a scalable classical approach to solving hard optimization problems and set a benchmark for quantum advantage.

## Contribution

The paper introduces probabilistic computers as a scalable classical alternative for real-world optimization and establishes a rigorous baseline for quantum advantage.

## Key findings

- Discrete-time simulated quantum annealing improves residual energy scaling with more replicas.
- Adaptive parallel tempering with non-local moves outperforms simulated quantum annealing.
- Probabilistic computing leverages hardware parallelism for efficiency and scalability.

## Abstract

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.

Probabilistic computing has emerged as a powerful route for tackling hard optimization. Here, authors show p-computers co-designed with modern hardware to run Monte Carlo algorithms solve hard optimization efficiently and establish a rigorous classical baseline to assess practical quantum advantage.