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| Quantum simulation of Hamiltonian in solid mechanics based on voxel representation |
| Received:May 03, 2025 Revised:June 06, 2025 |
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| DOI：10.7511/jslx20250503001 |
| KeyWord:quantum algorithm solid mechanics voxel mesh grids hamiltonian quantum circuit |
| Author | Institution |
| 吴锋 |
大连理工大学 力学与航空航天学院, 大连 |
| 李晨 |
大连理工大学 力学与航空航天学院, 大连 |
| 杨玉祥 |
大连理工大学 力学与航空航天学院, 大连 |
| 朱力 |
大连理工大学 力学与航空航天学院, 大连 |
| 郭旭 |
大连理工大学 力学与航空航天学院, 大连 |
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| Abstract: |
| 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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