面向在重六边形量子处理器上模拟二维哈伯德模型的硬件感知费米子-量子比特映射
Hardware-Aware Fermion-to-Qubit Mappings for Simulating the 2D Hubbard Model on Heavy-Hexagon Quantum Processors
浏览论文内容
中文总结 AI 辅助
该研究针对重六边形量子处理器，对比费米子-量子比特映射，证实Bonsai映射最适配，结合模拟退火优化后可在量子硬件上实现6×6格点二维哈伯德模型的高效模拟。
中文摘要 AI 辅助
强关联费米子系统的量子模拟是近期量子计算最具前景的应用之一，但其实际效率关键取决于费米子-量子比特映射的选择和底层硬件的连通性。本研究针对二维哈伯德模型，在具备重六边形连通性的IBM超导量子处理器上开展模拟，数值基准测试Jordan-Wigner、Bravyi-Kitaev和Bonsai三种变换，评估它们在7款尺寸递增的重六边形芯片上的泡利权重和SWAP开销。结果表明，尽管Bravyi-Kitaev映射初始泡利权重更低，但计入路由成本后该优势消失，证实Bonsai映射是该架构下最高效的硬件基准变换。随后，使用Bonsai映射构建二维自旋费米-哈伯德模型的量子比特哈密顿量，引入模拟退火算法优化马约拉纳串到格点的分配，使代价函数降低近50%。最后，在量子硬件上模拟6×6格点以内费米子态的时间演化，证实Bonsai编码适用于硬件感知的大规模二维模拟。
英文摘要
Quantum simulation of strongly correlated fermionic systems is among the most promising near- term applications of quantum computing, but its practical efficiency depends critically on the choice of fermion-to-qubit mapping and on the connectivity of the underlying hardware. In this work we address this problem in the context of the two-dimensional Hubbard model, simulated on IBM superconducting quantum processors with heavy-hexagon connectivity. We numerically benchmark the Jordan-Wigner, Bravyi-Kitaev, and Bonsai transformations, evaluating their Pauli weight and SWAP overhead across seven heavy-hexagon chips of increasing size. We show that, while the Bravyi-Kitaev mapping initially exhibits a lower Pauli weight, this advantage is eliminated once routing costs are taken into account, confirming the Bonsai mapping as the most hardware-efficient baseline transformation for this architecture. We then use the Bonsai mapping to construct the qubit Hamiltonian of the 2D spinful Fermi-Hubbard model, introducing a simulated annealing algorithm that optimizes the assignment of Majorana strings to lattice sites, reducing the cost function by nearly 50% percent. Finally, we simulate on quantum hardware the time evolution of fermionic states up to 6x6 lattices, confirming the viability of the Bonsai encoding for hardware-aware large-scale two-dimensional simulations.
