用量子与类量子算法求解刚体碰撞动力学问题。
Variational quantum and neural quantum states algorithms for the linear complementarity problem
- 将变分量子线性求解器与类量子神经网络结合，构建新求解框架。
- 在刚球碰撞模拟中实现高精度动态建模，验证算法可行性。
- 适合对物理系统仿真、量子算法应用感兴趣的科研人员。
变分量子算法（VQAs）是有望利用量子计算优势的混合量子-经典方法，同时缓解当前噪声中等规模量子（NISQ）硬件的局限性。尽管VQAs已作为概念验证展示，但其在解决实际问题中的实用性，以及量子启发的古典算法是否能媲美其性能，仍是未解之问。本文提出将变分量子线性求解器（VQLS）及其类量子神经态的对应方法——变分神经线性求解器（VNLS），作为基于互补性的刚体接触模型最小映射牛顿法的核心组件。通过使用VNLS，我们的求解器成功准确模拟了刚体球体碰撞过程中的动力学行为。结果表明，量子及量子启发的线性代数算法可成为建模特定物理系统的标准线性求解器的可行替代方案。
原文摘要 · Abstract (English)
Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems -- and whether quantum-inspired classical algorithms can match their performance -- remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modeling certain physical systems.
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