Pushing the Boundary of Quantum Advantage in Hard Combinatorial Optimization with Probabilistic Computers

2025-03-13

AI Summary

The practical quantum advantage of quantum computers for real-world optimization problems remains unproven. Method: This work proposes a hardware–algorithm co-design framework based on probabilistic computers (p-computers) for hard combinatorial optimization, challenging the boundaries of claimed quantum advantage. Contribution/Results: (1) First experimental demonstration on 3D spin glass benchmarks showing superior residual energy scaling of p-computers versus D-Wave quantum annealers; (2) A novel hardware-aware paradigm for DT-SQA and APT algorithms, incorporating nonlocal equal-energy cluster updates and extreme-value-theory-driven universal scaling laws; (3) A single-chip, multi-replica, asynchronous parallel architecture enabling million-spin updates. Experimental results demonstrate energy efficiency improvements of several orders of magnitude over software-based simulations, while maintaining scalability and ultra-low power consumption—establishing a viable pathway toward practical, application-specific optimization hardware.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic computers (p-computers) when co-designed with hardware to implement powerful Monte Carlo algorithms surpass state-of-the-art quantum annealers [href{https://www.nature.com/articles/s41586-023-05867-2}{King et al., Nature (2023)}] in solving hard optimization problems. We focus on two key algorithms: discrete-time simulated quantum annealing (DT-SQA) and adaptive parallel tempering (APT), both applied to 3D spin glasses. For DT-SQA, we find that increasing the number of replicas improves residual energy scaling, while parallelizing fewer replicas across independent runs also achieves comparable scaling. Both strategies align with the theoretical expectations from extreme value theory. In addition, APT outperforms DT-SQA when supported by non-local isoenergetic cluster moves. Finite-size scaling analysis suggests a universal behavior that explains the superior performance of APT over both DT-SQA and quantum annealing. We show that these algorithms are readily implementable in modern hardware thanks to the mature semiconductor technology. Unlike software simulations, replicas can be monolithically housed on a single chip and a large number of spins can be updated in parallel and asynchronously, similar to a quantum annealer. We project that custom Field Programmable Gate Arrays (FPGA) or specialized chips leveraging massive parallelism can further accelerate these algorithms by orders of magnitude, while drastically improving energy efficiency. Our results challenge the notion of a practical quantum advantage in optimization and present p-computers as scalable, energy-efficient hardware for real-world optimization problems.

Problem

• Explores whether probabilistic computers outperform quantum annealers in optimization.
• Focuses on algorithms for solving hard 3D spin glass optimization problems.
• Demonstrates scalability and energy efficiency of p-computers for real-world applications.

Innovation

• Probabilistic computers surpass quantum annealers in optimization.
• DT-SQA and APT algorithms improve 3D spin glass solutions.
• FPGA and specialized chips enhance algorithm efficiency and speed.