对称保持量子电路中的连通性控制变分可达性
Connectivity Controls Variational Accessibility in Symmetry-Preserving Quantum Circuits
- Jadavpur University（贾达普大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究揭示对称保持量子电路中生成器连通性决定变分可达性，通过最小修改连通性重建完整DLA，提升VQE基态保真度，提出扩大可访问多体空间的设计原则。
AI中文摘要：
设计用于变分量子本征求解器（VQE）的表达性量子电路是模拟相互作用多体系统中的一个核心挑战。即使是保持对称性（SP）的电路也不一定能访问完整的多体对称扇区。我们针对自旋-1/2 XXZ模型和Hubbard模型明确证明了这一点，其中受哈密顿量启发的最近邻（NN）SP电路生成了受限的动态李代数（DLA）。虽然这些受限流形可以准确表示自由费米子极限（XXZ的$J_z=0$和Hubbard的$U=0$）附近的基态，但相互作用暴露了不可访问的多体方向，即使在较大电路深度下也严重限制了VQE性能。值得注意的是，对生成器连通性的最小修改可以在本工作研究的所有相关对称扇区内重建完整的正交DLA。对于XXZ模型，仅添加一个SP次近邻（next-to-NN）单激发连接即可触发这种戏剧性的重建，而Hubbard模型则需要一个SP关联双激发；这表明相关连通性可以从空间晶格扩展到多体构型空间。这种重建扩大了切空间和对降能哈密顿量方向的可达性，导致VQE模拟中基态保真度接近单位。我们的结果建立了生成器连通性与变分可达性之间的直接联系，并提出了一个更广泛的电路设计原则：识别最小的对称保持生成器以扩大可访问的多体空间，而不是仅增加电路深度。这一视角可能对凝聚态物理与量子计算交叉领域的量子多体模拟具有更广泛的相关性。
英文摘要：
Designing expressive quantum circuits for the variational quantum eigensolver (VQE) is a central challenge in simulating interacting many-body systems. Even symmetry-preserving (SP) circuits need not access the full many-body symmetry sector. We demonstrate this explicitly for the spin-$1/2$ XXZ and Hubbard models, where Hamiltonian-inspired nearest-neighbor (NN) SP circuits generate restricted dynamical Lie algebras (DLAs). While these restricted manifolds can accurately represent the ground state near the free-fermion limits, $J_z=0$ for XXZ and $U=0$ for Hubbard, interactions expose inaccessible many-body directions and severely limit VQE performance even at large circuit depth. Remarkably, a minimal modification of the generator connectivity can reconstruct the full orthogonal DLA within all relevant symmetry sectors studied in this work. For XXZ model, the addition of {\it only} one SP next-to-NN single-excitation connection triggers this dramatic reconstruction, whereas the Hubbard case requires a SP correlated double-excitation;--showing that the relevant connectivity can extend from the spatial lattice to many-body configuration space. This reconstruction enlarges the tangent space and accessibility of the energy-lowering Hamiltonian direction, leading to near-unit ground-state fidelity in VQE simulations. Our results establish a direct link between generator connectivity and variational accessibility and suggest a broader circuit-design principle: identify minimal symmetry-preserving generators that enlarge the accessible many-body space rather than increasing circuit depth alone. This perspective may have broader relevance for quantum many-body simulation at the interface of condensed-matter physics and quantum computing.
