用于有效多体哈密顿量的自适应算子生成子空间
Adaptive operator-generated subspaces for effective many-body Hamiltonians
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中文总结 AI 辅助
本研究提出自适应克利福德代数子空间本征求解器A-CASE，通过共享泡利期望库重建矩阵、自适应增长子空间，实现从有效多体哈密顿量到能量等性质的计算，在基准测试中展现出与其他方法不同的精度与成本特性。
中文摘要 AI 辅助
电子结构与嵌入工作流最终会得到有效多体哈密顿量，而量子本征求解研究通常从手工构建的量子比特模型出发。我们提出了自适应克利福德代数子空间本征求解器（Adaptive Clifford-Algebra Subspace Eigensolver, A-CASE），这是一种单参考、算子生成的瑞利-里兹（Rayleigh--Ritz）方法。重叠矩阵、哈密顿矩阵、可观测量矩阵和响应矩阵均从一个共享的泡利（Pauli）期望库重建，而自适应增长过程会对感知重叠的局部束进行评分，并剔除对称泄漏或近似线性相关的部分。一个严格的FCIDUMP适配器提供活性空间边界。对于采用STO-3G基组、CAS(4e,4o)的线性H₄体系，映射得到的扇区与独立行列式全组态相互作用（FCI）的结果吻合至3.1×10⁻¹⁵ Ha。在9个矢量的预算下，A-CASE的误差为3.019 mHa；将行列式参考替换为双算子ADAPT-VQE态后，误差降至0.342 mHa，但这并不意味着总成本具有匹配优势。在匹配合约下，固定参考路线仅需1次态制备，而ADAPT-VQE需要90次，但前者测量的泡利项数量大约多一个数量级。精确固定角ADAPT-GCIM在最接近的规模匹配下误差为13.364 mHa，在迭代次数匹配下误差为10.674 mHa，其跃迁对负担另行报告。在更广泛的基准测试序列中，固定克雷洛夫（Krylov）基通常更准确，且往往更窄，但条件数明显更差。分组自助法通过阈值处理、对角化、根匹配、谱权重、磁化率和展宽传播有限采样的变异性；其区间明显是启发式和有条件的，并非有限样本置信证书。这项工作建立了一条从可互换哈密顿量到能量、关联和响应的可执行路径，但并未声称具备材料精度、有利的标度性或量子优势。
英文摘要
Electronic-structure and embedding workflows terminate in effective many-body Hamiltonians, whereas quantum eigensolver studies often start from hand-built qubit models. We present the Adaptive Clifford-Algebra Subspace Eigensolver (A-CASE), a single-reference, operator-generated Rayleigh--Ritz method. Overlap, Hamiltonian, observable, and response matrices are reconstructed from one shared Pauli-expectation bank, while adaptive growth scores overlap-aware local pencils and rejects symmetry leakage or near-linear dependence. A strict FCIDUMP adapter supplies the active-space boundary. For linear H$_4$ in STO-3G with CAS(4e,4o), the mapped sector agrees with independent determinant FCI to $3.1\times10^{-15}$ Ha. At a nine-vector budget A-CASE has a $3.019$ mHa error; replacing the determinant reference by a two-operator ADAPT-VQE state reduces it to $0.342$ mHa, without implying a matched total-cost advantage. Under a matched contract, the fixed-reference route uses one state preparation versus ADAPT-VQE's ninety but measures roughly an order of magnitude more Pauli words. Exact fixed-angle ADAPT-GCIM gives $13.364$ mHa at the nearest size match and $10.674$ mHa at the iteration match, with its transition-pair burden reported separately. Across a broader benchmark ladder, fixed Krylov bases are generally more accurate and often narrower but substantially less well conditioned. A grouped bootstrap propagates finite-shot variability through thresholding, diagonalization, root matching, spectral weights, susceptibility, and broadening; its bands are explicitly heuristic and conditional, not finite-sample confidence certificates. The work establishes an executable path from an interchange Hamiltonian to energies, correlations, and response, without claiming materials accuracy, favorable scaling, or quantum advantage.
