Since the quantum amplitude estimation (QAE) was invented by Brassard et al., 2002, several advanced algorithms have recently been published (Grinko et al., 2019, Aaronson et al, and Suzuki et al., 2020). The main difference between the variants and the original algorithm is that the variants do not need quantum phase estimation (QPE), a key component of the canonical QAE (Brassard et al., 2002), that is composed of many expensive operations on NISQ devices. In this paper, we compare and analyze two of these new QAE approaches (Grinko et al., 2019, and Suzuki et al., 2020) by implementation using the Qiskit package. The comparisons are drawn based on number of oracle queries, quantum circuit depth, and other complexities of implementation for a fixed accuracy. We discuss the strengths and limitations of each algorithm from a computational perspective.
Quantum Mechanics from Relational Properties, Part III: Path Integral Implementation
量子力学的关系表述是基于这样一种思想，即量子系统之间的关系性质，而不是量子系统的独立性质，是构造量子力学的最基本要素。在最近的一篇论文中（J. M. Yang，Sci. Rep. 8：13305，2018），基本的关系量子力学框架被制定为导出量子概率，玻恩规则，薛定谔方程和测量理论。本文从三个方面进一步扩展了重新表述的努力。首先，它对计算测量概率的框架背后的关键概念给出了更清晰的解释。其次，我们通过扩展路径积分公式，给出了关系概率幅的具体实现。该实现不仅阐明了关联几率幅的物理意义，而且使我们能够优雅地解释双缝实验，描述被测系统与一系列测量系统之间的相互作用历史，以及基于路径积分和影响泛函计算纠缠熵.作为回报，该实现通过完成对测量概率可以被计算为概率幅度的模平方的解释，为路径积分本身带来了新的见解。最后，我们阐明了我们的重新表述和量子参考系理论之间的联系。完整的量子力学关系式需要结合现有的工作和量子参考系理论。
Measurement-enabled online quantum processing with amplitude encoding
ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学与技术研究院）；Instituut-Lorentz, Universiteit Leiden（洛伦兹研究所，莱顿大学）；Applied Quantum Algorithms, Leiden University（莱顿大学应用量子算法）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
