基于比特串采样量子子空间的动态谱函数：采样成本由纠缠而非单体魔法追踪
Captured weight and boundary leakage bound the error of sample-based spectral functions
- Universidad Nacional de Colombia（哥伦比亚国立大学）
- SRH University（SRH大学）
- Daita AI
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究基于比特串采样浅实时电路的方法重构多种动态谱函数，发现采样成本由纠缠而非单体魔法追踪，相关方法可在IBM Heron处理器运行，自洽组态恢复能优化噪声下的子空间。
AI中文摘要：
基于采样的量子对角化（SQD）和量子选择组态相互作用（QSCI）是最受硬件青睐的电子结构方法，但其常规目标——基态能量——已被经典方法赶超。我们将目标转向动力学和资源问题：从一种比特串采样基础操作（浅实时电路的计算基测量，无需Hadamard门或受控幺正操作）出发，我们从采样子空间中重构了单粒子谱函数$A(\omega)$、$A(k,\omega)$，以及中性区动力学结构因子$S(q,\omega)$、$S^{zz}(q,\omega)$，每一项均在Lehmann表象中从各自子空间经典构建。该重构在Hubbard链上与精确对角化结果匹配，且对19个分子的$A(\omega)$（全组态相互作用FCI验证误差小于$10^{-5}$哈特里）也匹配，可在IBM Heron处理器上运行。其次，我们探究控制成本的资源：采样器必须填充的行列式支撑$|\mathcal{S}|$。在粒子数守恒态上，费米子AntiFlatness坍缩为一个单粒子约化密度矩阵（1-RDM）不变量$\mathcal{F}_1 = 4\\,\mathrm{tr}[\gamma(1-\gamma)] = 2N_u$。$\mathcal{F}_1$是轨道旋转（高斯）不变量，而$|\mathcal{S}|$依赖于基，$\mathcal{F}_1$已被证明与成本解耦；成本的下界及追踪由纠缠实现——最小键维度$\chi$（斯皮尔曼相关系数$\rho=0.90$）。因此，单体魔法是可靠的多参考诊断，但不可靠的成本预测因子；任何真正的优势存在于高阶累积量的非高斯性中。我们证明了矩精确性和与希尔伯特空间维度无关的$|\mathcal{S}|$多项式采样界。自洽组态恢复可在器件噪声下改进子空间，而学习生成模型未优于该经典基线。
英文摘要：
Rayleigh-Ritz on a subspace from sample-based quantum diagonalization yields the spectral function of a probe state; we ask what bounds its error. The captured Born weight w does not do so alone: an analytic counterexample forces any bound indexed on it to its trivial value. On Hubbard rings at broadening $η=0.18t$, the probe's whole support (w=1) still has relative error 0.35--0.43: Rayleigh-Ritz displaces the poles a subspace keeps. The error is bounded instead by the missed weight and the Hamiltonian coupling across the subspace boundary. Given the exact ground state, we prove for any orthogonal projector that the relative $L_1$ error lies between 1-w and $\min\{1+w,(1+\sqrt{w})(\sqrt{1-w}+Λ(η)/η)\}$, with $Λ$, that coupling at resolution $η$, computed from the Ritz pairs and the retained probe. We test it on L-site rings with classical Born draws of an exactly time-evolved probe, or their infinite-shot ranking; our device runs are execution records only. On the ranked subspaces the bound is vacuous at every operating fraction of the resource scan, at all five sizes up to a 10306296-determinant sector: its leakage branch exceeds the trivial bound 1+w by factors 1.66--8.61. It is informative only well above those fractions, where it is calibrated: at L=6--12 it first beats the trivial bound at a true error of (1.2--7.3)$\times10^{-3}$, though an unproven fit in 1-w is tighter on 11 of 14 splits. For the Born-ranked $A(k,ω)$ at 85% of its sector, the bound is 350--900 times the true error. In the determinant basis, zero leakage at full weight needs every symmetry-allowed determinant: the probe's measured Krylov support at L=6--14. Plane-wave orbitals reduce a momentum probe's support to one block, 1/L of an exponentially growing sector. At full weight a second-order certificate follows; below it, where every operating fraction lies, one is open.
