发表机构
Physical and Theoretical Chemistry Laboratory, University of Oxford（牛津大学物理与理论化学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明变分算法中能量收敛不能保证可观测量准确，误差可放大至$\sqrt{2\epsilon\chi_O}$，并在三种算法中验证了该认证失效现象。
AI 中文摘要
通过变分原理制备量子态的算法假设能量接近意味着态接近；我们通过证明基态能量估计收敛到真实值$\epsilon$范围内时，可观测量期望值的误差在领头阶可达$\sqrt{2\epsilon\chi_O}$，其中$\chi_O$是观测量的静态磁化率，从而形式化了这一假设可能失效的方式。因此，可观测量误差可能比能量误差大数个数量级，我们将此机制称为非线性误差放大；由于变分算法无法仅凭能量保证这些属性的正确性，能量并不必然认证可观测量。基于我们的发现，我们考察了三种算法：横向场伊辛链上的变分量子本征求解器、弱耦合氢分子链对上的密度矩阵重整化群，以及氟化锂上的Krylov量子对角化。在每种情况下，我们都证明了良好收敛的能量可能使可观测量未被认证。
英文摘要
Algorithms which prepare states via the variational principle assume that closeness in energy implies closeness in state; we formalise how this assumption can fail by showing that a ground-state energy estimate converged to within $ε$ of the true value is compatible with observable expectation values in error by up to $\sqrt{2εχ_O}$ at leading order, where $χ_O$ is the static susceptibility of the observable. As a result, the observable error can be orders of magnitude larger than the energy error, a mechanism we call non-linear error amplification, and because a variational algorithm cannot guarantee the correctness of these properties from energy alone, energy does not necessarily certify an observable. In light of our findings, we examine three algorithms: the variational quantum eigensolver on the transverse-field Ising chain, the density-matrix renormalisation group on a pair of weakly coupled hydrogen chains, and Krylov quantum diagonalisation on lithium fluoride. In each case we demonstrate that a well-converged energy can leave observables uncertified.
Comments10 pages, 4 figures
