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Quantum Computing Through Multi-Scale Modeling and Simulation

Jincheng Zhang

Published Sep 5, 2026• 0 citations
Publisher

Abstract

This paper presents a novel approach to quantum computing leveraging multi-scale modeling and simulation. The core claim is to develop a method capable of simultaneously simulating quantum systems at both microscopic and macroscopic levels, thereby enhancing the precision and efficiency of quantum computations. This is achieved through the construction of a multi-scale model integrating quantum mechanics and classical mechanics, coupled with advanced numerical simulation techniques. The proposed framework addresses the limitations of current quantum simulation methods by offering a more holistic representation of quantum systems. This allows for a deeper understanding of quantum phenomena and ultimately contributes to the advancement of quantum computing technologies. The key mathematical components utilized within this framework include the Schrödinger equation, perturbation theory, and various numerical integration schemes. Specifically, the time evolution of a quantum state is governed by the equation: (iħ ∂/∂t) |ψ(t)> = H |ψ(t)> where |ψ(t)> is the quantum state at time *t*, *ħ* is the reduced Planck constant, and *H* is the Hamiltonian operator. Perturbation theory, used to approximate the solution when the Hamiltonian is not solvable exactly, relies on the expansion: |ψperturbed>(t) = |ψunperturbed>(t) + ∑n=1∞ (-1)n+1 *An* |ψn>(t) where *An* are the perturbation coefficients. Numerical integration techniques, such as the Runge-Kutta method, are employed to approximate the time evolution operator. The accuracy of the simulation is critically dependent on the chosen time step, Δt, and the order of the integration method. A smaller Δt generally leads to higher accuracy but requires more computational resources. The overall approach seeks to bridge the gap between theoretical quantum mechanics and practical quantum computation, offering a viable path towards building more sophisticated and reliable quantum computers.

DOI
10.5281/zenodo.22338647

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This paper presents a novel multi-scale chaos simulation technique utilizing quantum simulation to enhance the accuracy and efficiency of existing chaos models. We propose a framework where a quantum simulation is employed to represent the dynamic evolution of a system across multiple scales, allowing for a more detailed and nuanced understanding of chaotic behavior. The core mechanism involves a sophisticated algorithm that iteratively evolves the quantum state, capturing the intricate interplay of quantum fluctuations within the system's dynamics. This approach addresses limitations in traditional chaos simulation methods by offering a pathway to investigate and quantify the fundamental principles governing complex systems. The research explores the potential for significant improvements in both simulation fidelity and computational cost. The findings demonstrate a substantial enhancement in the resolution of chaotic patterns, particularly at finer scales, compared to conventional methods.
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This paper presents a novel approach to non-linear system dynamics simulation utilizing quantum computing principles. Traditional simulation methods often struggle to effectively model complex systems due to computational limitations and inherent complexities. We introduce a quantum-enhanced simulation framework that leverages quantum mechanics to achieve unprecedented levels of accuracy and efficiency. The core mechanism involves a quantum-based model representation and a sophisticated optimization algorithm, designed to address the challenges inherent in simulating intricate dynamic systems. This work demonstrates the potential of quantum computing to revolutionize system dynamics modeling, offering a pathway to more precise and efficient simulations compared to classical methods. The paper explores the theoretical foundations of this approach, details the implementation of the simulation framework, and presents preliminary results showcasing the benefits of quantum-enhanced simulation.