Quantum Simulations of Classical Systems

Jincheng Zhang

Quantum simulation offers a revolutionary approach to understanding complex dynamical systems, enabling insights into emergent phenomena previously inaccessible through classical methods. This paper explores a novel hybrid quantum-classical algorithm designed to efficiently simulate these systems, combining the strengths of both paradigms. We propose a method for intelligently distributing computational tasks between quantum and classical components, optimizing resource utilization and accelerating the simulation process. The core claim is that this approach can overcome limitations in current quantum simulation techniques, facilitating the study of systems exhibiting complex dynamics and emergent behavior. This work presents a framework for seamless integration of quantum and classical algorithms, demonstrating its potential for significant advancements in the modeling and analysis of diverse dynamical systems.

Ilon Joseph, Alessandro R. Castelli, Vasily Geyko +6 more

David M. Ceperley

Cina Aghamohammadi, John R. Mahoney, James P. Crutchfield

Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators has recently come to the fore: they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems-in particular, the Dyson one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction range increases. In particular, simulating Dyson's original spin chain with the most memory-efficient classical algorithm known requires infinite memory, while a quantum simulator requires only finite memory. Thus, quantum systems can very efficiently simulate strongly coupled one-dimensional classical spin systems.

Cina Aghamohammadi, John R. Mahoney, James P. Crutchfield

Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators is that they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems---the Dyson-like one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction increases. Thus, quantum systems can very efficiently simulate strongly coupled classical systems.

Vijayarangan Natarajan