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Chinese Journal of Electronics

Exploring Potential Barrier Estimation Mechanism Based on Quantum Dynamics Framework

Quan Tang, Peng Wang

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Due to the probability characteristics of quantum mechanism, the combination of quantum mechanism and intelligent algorithm has received wide attention. Quantum dynamics theory uses the Schrödinger equation as a quantum dynamics equation. Through three approximation of the objective function, quantum dynamics framework (QDF) is obtained which describes basic iterative operations of optimization algorithms. Based on QDF, this paper proposes a potential barrier estimation (PBE) method which originates from quantum mechanism. With the proposed method, the particle can accept inferior solutions during the sampling process according to a probability which is subject to the quantum tunneling effect, to improve the global search capacity of optimization algorithms. The effectiveness of the proposed method in the ability of escaping local minima was thoroughly investigated through double well function (DWF), and experiments on two benchmark functions sets show that this method significantly improves the optimization performance of high dimensional complex functions. The PBE method is quantized and easily transplanted to other algorithms to achieve high performance in the future.

DOI
10.23919/cje.2023.00.293

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This work presents a quantum mechanical framework for analyzing quantization-based optimization algorithms. The sampling process of the quantization-based search is modeled as a gradient-flow dissipative system, leading to a Hamilton-Jacobi-Bellman (HJB) representation. Through a suitable transformation of the objective function, this formulation yields the Schroedinger equation, which reveals that quantum tunneling enables escape from local minima and guarantees access to the global optimum. By establishing the connection to the Fokker-Planck equation, the framework provides a thermodynamic interpretation of global convergence. Such an analysis between the thermodynamic and the quantum dynamic methodology unifies combinatorial and continuous optimization, and extends naturally to machine learning tasks such as image classification. Numerical experiments demonstrate that quantization-based optimization consistently outperforms conventional algorithms across both combinatorial problems and nonconvex continuous functions.
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This paper introduces a novel optimization technique, Quantum-Inspired Probabilistic Resonance (QIPR), designed to address the limitations of classical optimization algorithms when dealing with complex, multi-modal search spaces. Traditional methods often get trapped in local minima, hindering their ability to find global optima. QIPR leverages concepts from quantum mechanics, specifically superposition and interference, to probabilistically evaluate candidate solutions based on their "resonance" – the likelihood of escaping a local minimum. The algorithm employs a stochastic process influenced by these quantum principles, generating multiple candidate solutions and iteratively refining them based on their resonance scores. The core innovation lies in translating these quantum mechanical ideas into a practical probabilistic framework, offering a potentially more robust and efficient escape mechanism from complex optimization landscapes. The proposed method demonstrates promise in tackling challenging optimization problems where conventional techniques frequently fail. The evaluation process is fundamentally probabilistic, allowing for exploration of a wider solution space and increasing the probability of converging towards a global optimum. This work outlines the theoretical framework, the algorithm's implementation, and a preliminary discussion of its potential applications.
Quantum information materials, with their unique properties of quantum superposition, entanglement, topological protection, and quantum tunneling, provide a new physical foundation for quantum information science and technology. Based on the characteristics of quantum information materials, this paper proposes a novel optimization algorithm. This algorithm achieves a dynamic balance between global and local searches by simulating the superposition state of quantum amplitude and phase, combined with a triple mechanism of quantum entanglement attraction, topological barrier protection, and quantum tunneling perturbation. The algorithm utilizes amplitude and phase to jointly control the search process, ensuring the stability of excellent solutions while improving global exploration capabilities. This paper systematically elucidates the mathematical model, update mechanism, and core formulas of the algorithm, and discusses its theoretical innovation and potential application value.