从比特到量子比特：量子数据编码的理论与实践
From Bits to Qubits: The Theory and Practice of Quantum Data Encoding
- South China Normal University（华南师范大学）
- University of Oxford（牛津大学）
- Quantum Motion（量子运动）
- International Quantum Academy（国际量子学院）
- Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）
- Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
- Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）
- Mathematical Institute, University of Oxford（牛津大学数学研究所）
- Peking University（北京大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本综述系统梳理量子数据编码的概念、算法与实践，涵盖量子态制备、酉合成、QRAM和块编码等访问模型，分析电路规模、容错资源及结构化数据编码，为研究者提供教学与参考，并展望实现量子优势的未来方向。
AI中文摘要：
将经典数据编码到量子系统中是几乎所有量子算法执行的基础步骤，也是实现实用量子优势的关键瓶颈。本综述全面阐述了与量子数据编码相关的概念、算法和实际考量。我们追溯了从早期概念基础到近期进展的发展历程，考虑了常用的访问模型，如量子态制备、酉合成、QRAM和块编码。我们调研了电路规模、深度、时空权衡，以及容错实现所需的非Clifford资源。我们还讨论了不同访问模型在量子算法中的作用。特别关注结构化数据，如稀疏数据、布尔函数和张量网络表示的数据。本综述弥合了理论与应用之间的鸿沟，既作为新入门者的教学指南，也作为活跃研究者的参考。我们还强调了量子数据编码在量子计算中的关键作用，并展望了未来实现量子优势的方向。
英文摘要：
Encoding classical data into quantum systems is a foundational step in the execution of nearly all quantum algorithms, and a critical bottleneck in realizing practical quantum advantage. This review provides a comprehensive account of the concepts, algorithms, and practical considerations associated with quantum data encoding. We trace the development from its early conceptual foundations to recent advances, considering commonly used access models, such as quantum state preparation, unitary synthesis, QRAM and block encoding. We survey the circuit size, depth, space-time tradeoffs, as well as non-Clifford resources required for fault-tolerant implementation. We also discuss the roles of different access models in quantum algorithms. Special attention is given to structured data, such as sparse data, Boolean functions and data represented by tensor networks. This review bridges theory and applications, serving both as a pedagogical guide for newcomers and as a reference for active researchers. We also highlight the pivotal role of quantum data encoding in quantum computing and provide insights into future directions that will enable quantum advantage.
