高效哈密顿量截断：快速矩阵构造与量子Krylov对角化
Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization
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中文总结 AI 辅助
针对哈密顿量截断中希尔伯特空间扩张导致的计算成本过高问题，该研究采用经典-量子混合策略，通过整数分拆基生成、对称感知矩阵构造及量子Krylov对角化提升效率，在二维场论基准中取得显著进展。
中文摘要 AI 辅助
哈密顿量截断为量子场论提供了一种非微扰途径，但其精度受限于截断希尔伯特空间的快速扩张，这会推高计算成本。我们采用经典与量子算法结合的混合策略解决这一瓶颈：1）开发基于整数分拆的高效基生成方案；2）使用感知对称性的算法加快稀疏哈密顿量矩阵的构造；3）探索量子Krylov对角化以求解低能谱。通过对比二维时空的自由有质量标量场与φ⁴理论，我们在哈密顿量截断的计算效率上实现了显著提升，并为未来的量子实现指明了方向。
英文摘要
Hamiltonian truncation offers a nonperturbative route to quantum field theory, yet its accuracy is limited by the rapid expansion of the truncated Hilbert space, which drives up computational cost. We tackle this bottleneck with a hybrid strategy that pairs classical and quantum algorithms: 1) we develop an efficient basis-generation scheme built on integer partitions; 2) we speed up the construction of the sparse Hamiltonian matrix using symmetry-aware algorithms; and 3) we explore quantum Krylov diagonalization as a route to the low-lying spectrum. Benchmarking against the free massive scalar and $ϕ^4$ theories in two spacetime dimensions, we achieve substantial gains in the computational efficiency of Hamiltonian truncation and chart a path toward future quantum implementations.
