AI 中文总结
本文针对arXiv:2607.24014v1的三重态块读出经典成本主张，提出O(n⁴)确定性算法，推翻其指数成本结论，且不影响其他相关结果。
AI 中文摘要
我们考察arXiv:2607.24014v1中关于三重态块两体读出的经典成本主张。该研究使用的高斯态展开给出了O(2^(2k/3)poly(n))的经典算法，但对于固定体可观测量而言并非必要。三重态块输入具有可显式计算的对角两粒子约化密度矩阵，无源费米子线性光学将其通过∧²W传播，这为完整关联向量（⟨n_i n_j⟩）_{i<j}提供了确定性的O(n⁴)算法，且与k及费米子线性光学的范围无关。更一般地，只要输入的r粒子约化密度矩阵可经典获取，每个守恒粒子数的固定r体期望值都可多项式计算；若该矩阵为对角矩阵，则所有对角关联函数均可在O(n^(2r))时间内计算。这推翻了有监督两体读出的算法相关指数成本结论，但不影响梯度方差、贫瘠高原、参数偏移或采样硬度结果。
英文摘要
We examine the classical-cost claim for the triplet-block two-body readout in arXiv:2607.24014v1. The Gaussian-state expansion used there gives an $O(2^{2k/3}\mathrm{poly}(n))$ classical algorithm, but it is not necessary for fixed-body observables. The triplet-block input has an explicitly computable diagonal two-particle reduced density matrix, which passive fermionic linear optics propagates through $\bigwedge^2 W$. This gives a deterministic $O(n^4)$ algorithm for the complete correlator vector $(\langle n_i n_j\rangle)_{i<j}$, independently of $k$ and the fermionic-linear-optics extent. More generally, every number-conserving fixed-$r$-body expectation is polynomially computable whenever the input $r$-particle reduced density matrix is classically available; if that matrix is diagonal, all diagonal correlators are computable in $O(n^{2r})$ time. This invalidates the algorithm-relative exponential-cost conclusion for the supervised two-body readout, without affecting the gradient-variance, barren-plateau, parameter-shift, or sampling-hardness results.
Comments3 pages, no figures. Comment on arXiv:2607.24014v1
