论文标题
节俭的阴影估计：重复使用量子电路和边界尾巴
Thrifty shadow estimation: re-using quantum circuits and bounding tails
论文作者
论文摘要
影子估计是一种最新的协议，可以从``经典阴影''量估计量子状态的许多期望值，该量子是通过应用随机量子电路和计算基础测量来获得的。在本文中，我们根据近期量子计算研究了这种方法的统计效率。我们提出了一个更实用的协议，节俭的影子估计，其中量子电路被重复了多次，而不必为每个测量而新鲜生成。我们表明，在对HAAR随机单位进行采样时，重复使用是最大有效的，并且当从Clifford组采样时，即在与Clifford组执行阴影估计时不应重复使用电路。我们提供了有效模拟的量子电路家族，它们在这些极端之间进行了插值，我们认为应该将其代替Clifford组。最后，我们考虑用于阴影估计的尾巴界限，并讨论何时可以用标准平均估计代替均值估计。
Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this paper we study the statistical efficiency of this approach in light of near-term quantum computing. We propose a more practical variant of the protocol, thrifty shadow estimation, in which quantum circuits are reused many times instead of having to be freshly generated for each measurement. We show that reuse is maximally effective when sampling Haar random unitaries, and maximally ineffective when sampling from the Clifford group, i.e., one should not reuse circuits when performing shadow estimation with the Clifford group. We provide an efficiently simulable family of quantum circuits that interpolates between these extremes, which we believe should be used instead of the Clifford group. Finally, we consider tail bounds for shadow estimation and discuss when median-of-means estimation can be replaced with standard mean estimation.
