DA-CASE：自适应量子子空间的可复用测量
DA-CASE: reusable measurements for adaptive quantum subspaces
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中文总结 AI 辅助
该研究提出DA-CASE方法，以单参考测量架构及资源账本实现量子子空间的可复用测量，在小实例中优化了测量设置等资源并降低了投影矩阵方差。
中文摘要 AI 辅助
量子子空间方法常通过基矢维度或能量误差进行比较，但其主要实验成本源于不同的态制备、测量设置及 shots（采样次数）分配。我们提出双自适应克利福德代数子空间本征求解器（Dyadic Adaptive Clifford-Algebra Subspace Eigensolver，DA-CASE），其基矢态为从单个参考态|ψ⟩生成的虚拟方向Aᵢ|ψ⟩，哈密顿量与可观测量矩阵均通过对该参考态的一组缓存泡利算符期望值重构。该方法以潜在更宽的测量范围替代多个制备的基矢态，我们在冻结的8量子比特H₄哈密顿量上明确该权衡：两种生成器分辨率达到相同的9维子空间和机器精度下的相同能量，保留的泡利词库从7371变为2240；参考条件对称性测试在不断言单个泡利词作为抽象算符守恒扇区的情况下，认证了更窄的张成空间。此外，双对易层级将行列式库从913个逐量子比特对易设置缩减为64个完全对易设置，同时揭示了额外的逻辑-CX门成本。在单独的4量子比特有限shots诊断中，协方差感知分配将投影矩阵方差目标降低68.9%；模式-wise重叠正则化消除了观测到的灾难性能量估计并降低了均方根误差（RMSE），但相对于固定截断值使中位数误差翻倍。这些是小实例的精确结果与蒙特卡洛结果，非硬件演示、可扩展性结果或量子优势主张，贡献为单参考测量架构及资源账本，其将上下文、设置、shots、电路深度与后选择重试保持在恰当单位中。
英文摘要
Quantum subspace methods are often compared by basis dimension or energyerror, although their dominant experimental costs arise from different statepreparations, measurement settings, and shot allocations. We present theDyadic Adaptive Clifford-Algebra Subspace Eigensolver (DA-CASE), whose basisstates are virtual directions $A_i|ψ\rangle$ generated from one reference.Overlap, Hamiltonian, and observable matrices are reconstructed from onecached set of Pauli expectations on that reference. The method thereforetrades multiple prepared basis states for a potentially wide measurement bank.We make that trade explicit on a frozen eight-qubit H$_4$ Hamiltonian. Twogenerator resolutions reach the same nine-dimensional subspace and the sameenergy to machine precision, while the retained bank changes from 7371 to 2240Pauli words. A reference-conditioned symmetry test certifies the narrower spanwithout asserting that its individual Pauli words conserve the sector asabstract operators. Independently, a dyadic commuting hierarchy reduces thedeterminant bank from 913 qubit-wise-commuting settings to 64 fully commutingsettings, while exposing the added logical-CX cost. In a separate four-qubitfinite-shot diagnostic, covariance-aware allocation reduces theprojected-matrix variance target by 68.9%. Mode-wise overlap regularizationremoves the observed catastrophic energy estimates and lowers RMSE, butdoubles the median error relative to a fixed cutoff. These are small-instanceexact and Monte Carlo results, not a hardware demonstration, scaling result,or quantum advantage claim. The contribution is a single-referencemeasurement architecture and a resource ledger that keeps contexts, settings,shots, circuit depth, and post-selection retries in their proper units.
