Quantum mechanics simulated by diffusion and branching processes

R. Eugene Collins

Fricke, Thomas

Diffusion processes with branching play an important role in statistical dynamics. They are a common approach to the computing of quantum mechanical groundstates, and serve as models for population dynamics and as physical pictures for biological evolution. On a computer the efficiency of this simulation method is limited by the approach to the infinitesimal time step, which is necessary to perform alternating diffusion and branching steps. In this paper, a method is described, which eliminates the infinitesimal time step for a certain class of branching processes, if the process of interest can be ``embedded'' into another process, which is solvable by other analytic and/or numerical methods. The simplest choice for the embbeding process is given by a process with a constant branching rate, which dominates the rate of the embedded process.

John R. Hiller, Ian Johnston, Daniel F. Styer +3 more

Jincheng Zhang

Quantum-enhanced diffusion is a novel approach to accelerating molecular dynamics simulations by leveraging quantum mechanics to model the diffusion process. This paper explores the potential of quantum algorithms to overcome the inherent limitations of classical methods, ultimately achieving more accurate and efficient simulations. We detail the core mechanism, outlining the theoretical foundation and practical implementation of this quantum-accelerated diffusion technique. The goal is to demonstrate a significant improvement in simulation speed compared to existing classical methods, particularly for complex molecular systems exhibiting diffusion behavior. The paper concludes with a discussion of the challenges and future research directions.

Folkert Kuipers

Jincheng Zhang

Quantum-Enhanced Diffusion Modeling with Adaptive Kernel (QEDM-K) presents a novel approach to diffusion modeling by integrating quantum-inspired kernels to address limitations of existing methods. This research explores the application of these kernels to improve the accuracy and speed of simulating diffusion processes. The core mechanism centers around leveraging the inherent randomness captured within quantum mechanics to enhance the representation of diffusion patterns. This results in a more robust and efficient modeling process, particularly for complex scenarios. This paper details the theoretical underpinnings of the QEDM-K framework, presents a comprehensive implementation demonstrating its efficacy, and discusses potential future research directions.