发表机构
Tata Institute of Fundamental Research; University of Southampton; Central China Normal University（塔塔基础研究所; 南安普顿大学; 华中师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究保持局域性的DK费米子-量子比特映射，结合约束保持的Clifford态制备与对称性保持的变分电路，实现高维相互作用费米子模型的资源高效量子模拟。
AI 中文摘要
我们研究了保持局域性的Derby-Klassen（DK）费米子到量子比特映射[arXiv:2003.06939]在二维$t$-$V$模型和Fermi-Hubbard模型的变分量子模拟中的实用性。DK映射通过扩大希尔伯特空间来保持费米子相互作用的局域性，因此需要额外的约束来定义物理扇区。我们通过Clifford门态制备将这些约束直接纳入哈密顿量变分拟设（HVA），并使用变分量子本征求解器（VQE）证明由此产生的量子比特哈密顿量的低能性质能被准确重现。我们进一步利用拟设中固有的粒子数守恒来解析不同的对称性扇区，并可靠地访问简并态。因此，我们在非零化学势下将DK-HVA与基于Jordan-Wigner的变分电路进行基准比较，此时粒子-空穴对称性及相关的半填充无符号条件不存在。最后，我们展示了保持局域性的映射在高维费米子系统中的优势，其中传统的Jordan-Wigner（JW）变换会产生越来越长的Pauli字符串及相应的电路开销。我们进一步将该框架扩展到自旋费米Hubbard模型，并识别出费米子模式放置与跳跃项和局域相互作用项局域性之间的权衡。这些结果建立了一个实用的框架，结合了保持局域性的费米子到量子比特映射、保持约束的Clifford态制备和保持对称性的变分电路，以辅助量子比特和稳定子制备开销换取减少的算符非局域性，为高维相互作用费米子系统的资源高效量子模拟提供了实用途径。
英文摘要
We investigate the utility of the locality-preserving Derby-Klassen (DK) fermion-to-qubit mapping [arXiv:2003.06939] for variational quantum simulation of two-dimensional $t$-$V$ and Fermi-Hubbard models. The DK mapping preserves the locality of fermionic interactions with an enlarged Hilbert space, thereby requiring additional constraints that define the physical sector. We incorporate these constraints directly into a Hamiltonian Variational Ansätz (HVA) through Clifford-gate state preparation and use the Variational Quantum Eigensolver (VQE) to show that the low-energy properties of the resulting qubit Hamiltonian are accurately reproduced. We further exploit particle-number conservation inherent in the ansätz to resolve distinct symmetry sectors and reliably access degenerate states. Consequently, we benchmark the DK-HVA against Jordan-Wigner-based variational circuits at nonzero chemical potential, where particle-hole symmetry and the associated half-filled sign-free condition are absent. Finally, we demonstrate the advantage of locality-preserving mappings in higher-dimensional fermionic systems, where the conventional Jordan-Wigner (JW) transformation generates increasingly long Pauli strings and corresponding circuit overheads. We further extend the framework to the spinful Fermi-Hubbard model and identify a tradeoff between fermionic-mode placement and the locality of hopping and on-site interaction terms. These results establish a practical framework combining locality-preserving fermion-to-qubit mappings, constraint-preserving Clifford state preparation, and symmetry-preserving variational circuits, that trades auxiliary-qubit and stabilizer-preparation overhead for reduced operator nonlocality, providing a practical route toward resource-efficient quantum simulation of higher-dimensional interacting fermionic systems.
Comments19 pages, 20 figures, 4 tables
