非稳定子性增强节俭阴影估计
Nonstabilizerness Enhances Thrifty Shadow Estimation
AI总结：
本研究揭示基于2-设计酉系综的节俭阴影估计平均有效，发现其方差与非稳定子性负相关、随稳定子2-Rényi熵指数下降，并提出仅含一层T门的高效电路，为NISQ时代的量子估计提供了资源更省的方案。
摘要：
阴影估计是一种用于估计多个可观测量期望值的强大方法。节俭阴影估计是一种简单的变体，旨在通过重复使用随机电路来降低实验开销。尽管这一思路非常简单，但其性能却相当难以捉摸。在本研究中我们证明，只要酉系综构成2-设计，节俭阴影估计平均而言就是有效的，这与此前的预期形成鲜明对比。在基于Clifford群的节俭阴影估计中，方差与量子态及可观测量的非稳定子性程度呈负相关，而非稳定子性是量子信息处理中的关键资源。对于保真度估计，其方差随目标态的稳定子2-Rényi熵呈指数下降，这赋予了稳定子2-Rényi熵明确的操作意义。此外，我们提出了一种可提升效率的简单电路，该电路仅需一层$T$门，在NISQ（含噪声中等规模量子）时代极具吸引力。
英文摘要：
Shadow estimation is a powerful approach for estimating the expectation values of many observables. Thrifty shadow estimation is a simple variant that is proposed to reduce the experimental overhead by reusing random circuits repeatedly. Although this idea is so simple, its performance is quite elusive. In this work we show that thrifty shadow estimation is effective on average whenever the unitary ensemble forms a 2-design, in sharp contrast with the previous expectation. In thrifty shadow estimation based on the Clifford group, the variance is inversely correlated with the degree of nonstabilizerness of the state and observable, which is a key resource in quantum information processing. For fidelity estimation, it decreases exponentially with the stabilizer 2-Rényi entropy of the target state, which endows the stabilizer 2-Rényi entropy with a clear operational meaning. In addition,we propose a simple circuit to enhance the efficiency, which requires only one layer of $T$ gates and is particularly appealing in the NISQ era.
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