实用费米子阴影：通过改进样本复杂度界实现

中文摘要 AI 辅助

经典阴影层析被广泛认为提供了一系列从量子系统中提取信息的方法，其样本复杂度呈多项式增长。然而，在当前拥有数百量子比特的量子计算机时代，多项式增长仍然可能令人望而却步。因此，获得尽可能紧的样本复杂度界具有强烈的实际需求。在此，我们针对费米子（匹配门）阴影处理这一问题。对于任意马约拉纳度为 $2k$ 的可观测量 $O$，我们将先前已知的样本复杂度界 $\nathcal{O}(n^{2k}\n|O\|_\ninfty^2)$ 改进为 $\nathcal{O}(n^{k}\n|O\|_\ninfty^2)$，该界是渐近紧的。例如，对于具有跳跃强度和位点强度分别为 $t=1$、$V=4$ 的开放费米子 50 位点 Hubbard 链的每模能量估计，以及目标加性精度为 0.1，所需射击次数从约 $10^9$ 减少到约 $10^5$。也就是说，新界将所需射击次数减少了约 $99.98\%$。

英文摘要

Classical shadow tomography is widely touted as supplying a family of methods for extracting information from quantum systems with polynomially scaling sample-complexities. In the current era of quantum computers possessing on the order of hundreds of qubits, however, polynomial scaling can nonetheless be prohibitive. Thus, there is a strong practical need for obtaining sample-complexity bounds which are as tight as possible. Here we address this in the case of fermionic (matchgate) shadows. For an arbitrary observable $O$ of Majorana degree $2k$, we improve the previously known sample-complexity bound of $\mathcal{O}(n^{2k}\|O\|_\infty^2)$ to $\mathcal{O}(n^{k}\|O\|_\infty^2)$, which is asymptotically tight. For example, for the estimation of the energy per mode of an open fermionic 50-site Hubbard chain with hopping and on site strenghts respectively given by $t=1$, $V=4$, and for a target additive precision of 0.1, this reduces the number of required shots from $\sim 10^9$ to $\sim 10^5$. That is, the new bound reduces the required number of shots by approximately $99.98\%$.

发表机构

• Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
• Quantum Science Center, Oak Ridge, TN 37931, USA（橡树岭量子科学中心）
• Harvard University（哈佛大学）

机构由 AI 辅助整理，请以论文原文为准。