用浅层电路高效学习多个非对易量子算符，提升化学能级与多体系统验证精度。
Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits
- 通过浅层电路旋转测量基，结合张量网络控制计算开销。
- 在量子化学基准上样本复杂度显著低于现有方法。
- 适合需要估计多个非对易算符的量子算法集成使用。
高效估计大量非对易可观测量是众多量子科学任务的关键步骤。本文提出去随机化浅层阴影（DSS）算法，利用浅层电路将系统旋转至测量基，实现对一组非对易泡利字符串的高效学习。通过张量网络技术保障经典资源的多项式增长，该算法输出一组浅层测量电路，近似最小化给定泡利字符串集合的样本复杂度。数值实验表明，在量子化学基准的能量估计和多体系统验证任务中，相比当前最优方法有系统性提升；且随着允许的测量电路深度增加，性能持续改善。结果表明，DSS不仅是一种高效、低深度的独立算法，还可为需估计多个非对易可观测量的大型量子算法提供支持。
原文摘要 · Abstract (English)
Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.
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