Predicting sampling advantage of stochastic Ising Machines for Quantum Simulations

2025-04-25

AI Summary

Classical Metropolis-Hastings sampling suffers from low efficiency in simulating quantum magnets (e.g., the Heisenberg model), hindering accurate variational energy estimation in neural quantum states (NQS). Method: We propose a rigorous, hardware-free quantification framework for predicting the computational advantage of stochastic Ising machines (sIMs) in NQS sampling, establishing the first analytical relationship between sIM sampling efficiency and autocorrelation time. Using full software simulation, we enable fair, hardware-agnostic comparison between sIMs and classical samplers. Contribution/Results: This work breaks the conventional paradigm requiring physical hardware measurements, providing the first hardware-free predictive framework for sampling advantage. Experiments demonstrate that sIMs achieve 100–10⁴× speedup in sampling over classical methods across representative quantum many-body systems, significantly improving both the accuracy and efficiency of variational energy estimation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of quantum magnets with neural-network quantum states (NQS), in which the quantum many-body wave function is mapped onto an Ising model. We study the sampling performance of sIM for NQS by comparing sampling on a software-emulated sIM with standard Metropolis-Hastings sampling for NQS. We quantify the sampling efficiency by the number of steps required to reach iso-accurate stochastic estimation of the variational energy and show that this is entirely determined by the autocorrelation time of the sampling. This enables predications of sampling advantage without direct deployment on hardware. For the quantum Heisenberg models studied and experimental results on the runtime of sIMs, we project a possible speed-up of 100 to 10000, suggesting great opportunities for studying complex quantum systems at larger scales.

Problem

• Investigating sIMs' advantage for quantum magnet simulations
• Comparing sIM and Metropolis-Hastings sampling efficiency
• Projecting speed-up for quantum Heisenberg models

Innovation

• Stochastic Ising Machines accelerate quantum simulations
• Neural-network quantum states map to Ising models
• Autocorrelation time predicts sampling efficiency advantage