发表机构
Rensselaer Polytechnic Institute; IBM Quantum, IBM T.J. Watson Research Center（伦斯勒理工学院; IBM量子，IBM T.J.沃森研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨了基于采样的量子对角化中基态选择对费米-哈伯德梯子计算效率的影响，发现基态可压缩性随相互作用和跳跃各向异性变化，并指出可扩展性需协同设计采样表示、量子电路和经典重建。
AI 中文摘要
基于采样的量子对角化可以通过将对角化限制在通过量子采样确定的构型上，降低多体计算的经典成本，但其效率取决于目标态在采样基态中表示的紧凑程度。我们研究了半填充费米-哈伯德梯子的基于采样的Krylov量子对角化对此依赖关系，采用物理动机的单体轨道旋转。在位置、动量、成键/反键和腿模表示中，最可压缩的基态随相互作用强度和跳跃各向异性系统性地变化，动量采样在弱相互作用区域受青睐，而几何或相互作用适应的表示在主导能量尺度变化时变得有利。然而，在中等相互作用和各向同性跳跃附近，即使最有利的表示也仍然难以压缩。态矢量SKQD计算进一步表明，基态选择强烈影响采样效率。对包含多达120个量子比特的系统的硬件计算保留了这种基态依赖的定性特征，同时揭示了随系统尺寸增加的粒子数泄漏和重建敏感性。这些结果表明，可扩展的基于采样的对角化需要采样表示、量子电路和经典重建过程的协同设计。
英文摘要
Sample-based quantum diagonalization can reduce the classical cost of many-body calculations by restricting diagonalization to configurations identified through quantum sampling, but its efficiency depends on how compactly the target state is represented in the sampled basis. We investigate this dependence for sample-based Krylov quantum diagonalization of the half-filled Fermi-Hubbard ladder using physically motivated one-body orbital rotations. Across position, momentum, bonding/antibonding, and leg-mode representations, the most compressible basis varies systematically with interaction strength and hopping anisotropy, with momentum sampling favored in the weakly interacting regime and geometry- or interaction-adapted representations becoming advantageous as the dominant energy scale changes. Near intermediate interaction and isotropic hopping, however, even the most favorable representation remains poorly compressible. Statevector SKQD calculations further show that basis choice strongly affects sampling efficiency. Hardware calculations on systems containing up to 120 qubits retain qualitative signatures of this basis dependence while revealing increasing particle-number leakage and reconstruction sensitivity with system size. These results show that scalable sample-based diagonalization requires co-design of the sampled representation, quantum circuit, and classical reconstruction procedure.
