| 吴锋,李晨,杨玉祥,朱力,郭旭.基于体素表示的固体力学哈密顿量的量子模拟[J].计算力学学报,2025,42(3):329~338 |
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| 基于体素表示的固体力学哈密顿量的量子模拟 |
| Quantum simulation of Hamiltonian in solid mechanics based on voxel representation |
| 投稿时间：2025-05-03 修订日期：2025-06-06 |
| DOI：10.7511/jslx20250503001 |
| 中文关键词: 量子算法 固体力学 体素网格 哈密顿量 量子电路 |
| 英文关键词:quantum algorithm solid mechanics voxel mesh grids hamiltonian quantum circuit |
| 基金项目:国家自然科学基金(12372190;6238810)资助项目. |
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| 摘要点击次数: 29 |
| 全文下载次数: 11 |
| 中文摘要: |
| 量子模拟是解决大规模力学计算面临的效率和存储量瓶颈的重要手段,然而如何对空间离散后的厄米矩阵进行有效分解仍是力学问题量子模拟的关键难题之一。本研究以体素网格离散求解域,深入剖析所得矩阵(记为体素网格矩阵)结构特性,创新性提出KCQ分解方法。该方法融合循环矩阵、矩阵直积、直和以及泡利矩阵等数学手段,能够将体素网格矩阵分解为k n, c n, q n三组基本矩阵。基于KCQ分解,结合量子傅里叶变换、量子多路选择器等技术,进一步构建出针对体素网格矩阵的高效哈密顿量的量子模拟算法。通过二维非均质板自由振动问题的模拟实验,验证了构建的量子算法的正确性和有效性,为固体力学问题的量子模拟提供了新的方法支撑。 |
| 英文摘要: |
| Quantum simulation has emerged as a crucial approach to overcoming the bottlenecks of computational efficiency and storage capacity in large-scale mechanical calculations.However,the effective decomposition of Hermitian matrices obtained after spatial discretization remains one of the key challenges in the quantum simulation of mechanical problems.In this study,the solution domain is discretized using voxel grids,and the structural properties of the resulting matrices (referred to as voxel grid matrices) are thoroughly analyzed.An innovative KCQ decomposition method is proposed,which integrates mathematical techniques such as circulant matrices,matrix direct products,direct sums,and Pauli matrices.It enables the decomposition of voxel grid matrices into three sets of basic matrices,namely kn,cn,qn.Based on the KCQ decomposition,combined with technologies such as quantum Fourier transform and quantum multiplexers,an efficient Hamiltonian quantum simulation algorithm for voxel grid matrices is further constructed.The correctness and effectiveness of the proposed quantum algorithm are verified through simulation experiments on the free vibration of two-dimensional heterogeneous plates,providing a novel methodological support for the quantum simulation of solid mechanics problems. |
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