资源高效的量子行走量子随机存取存储器的技术分析
Technical analysis of the Resource-efficient Quantum Walkers Quantum Random Access Memory
- Scuola Normale Superiore（比萨高等师范学院）
- NEST-CNR Scuola Normale Superiore（NEST-意大利国家研究委员会比萨高等师范学院）
- Dept. of Mech. Eng., Massachusetts Institute of Technology（麻省理工学院机械工程系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文对基于离散时间量子行走的资源高效qRAM进行技术分析，提出长程与短程两种算法范式，其中短程方法通过分解为局部门实现最优电路深度，并探索多种量子行走器类型。
AI中文摘要：
量子随机存取存储器（qRAM）是算法中实现量子优势的关键组件，其应用范围从数据库搜索到量子机器学习。在最近提出的模型[arXiv:2508.02855]中，我们提出了一种基于离散时间量子行走的资源高效qRAM架构。本文作为全面的技术后续，提供了完整的数学推导、详细的协议规范以及深入的资源分析。此外，我们扩展了原始提案，引入了新技术以使qRAM的实现更加现实。我们的模型解决了领先qRAM提案的主要缺陷：它避免了“桶队列”架构所需的指数级活动节点数$\mathcal{O}(2^n)$，而是采用量子行走器，其数量与地址和消息大小（分别为$n$和$m$）线性扩展。同时，它通过消除对多个并行树的需求，克服了先前量子行走方案的空间瓶颈。我们提出了两种算法范式：长程和短程方法，它们的主要区别在于qRAM中采用的主路由门的相互作用长度。我们形式化了两种变体的路由、消息复制和行走器检索阶段，并展示了长程方案采用具有多个目标系统的受控门，而短程方法将这些相互作用分解为2体和3体局部门的序列，这提高了架构在近期实验实现中的可行性。最后，我们全面的资源分析证实，短程方法实现了最优的$\mathcal{O}(n+m)$电路深度。在这两种范式中，我们探索了不同类型的量子行走器的潜力，即玻色子、双轨量子比特和四能级量子比特。
英文摘要：
Quantum Random Access Memory (qRAM) is a critical component for achieving quantum advantage in algorithms ranging from database search to quantum machine learning. In a recently introduced model [arXiv:2508.02855], we proposed a resource-efficient qRAM architecture based on discrete-time quantum walkers. This article serves as a comprehensive technical follow-up, providing the full mathematical derivations, detailed protocol specifications, and in-depth resource analysis. Moreover, we extend the original proposal with novel techniques for the purpose of making the qRAM implementation more realistic. Our model resolves the primary drawbacks of leading qRAM proposals: it avoids the exponential number of active nodes $\mathcal{O}(2^n)$ required by the "Bucket Brigade" architecture by employing a number of quantum walkers that scales linearly with the address and message sizes, $n$ and $m$, respectively. Simultaneously, it overcomes the spatial bottlenecks of previous quantum-walker schemes by eliminating the need for multiple parallel trees. We propose two algorithmic paradigms: the long- and the short-range approaches, which differ by the length of interaction of the main routing gates employed in the qRAM. We formalize the routing, message-copy, and walker retrieval phases for both variants and we show how, while the long-range scheme employs controlled gates having a multitude of target systems, the short-range approach decomposes these interactions into sequences of 2- and 3-body local gates, which improves the architecture's feasibility for near-term experimental implementation. Finally, our comprehensive resource analysis confirms that the short-range approach achieves the optimal $\mathcal{O}(n+m)$ circuit depth. Within these two paradigms, we explore the potential of different types of quantum walkers, namely bosons, dual-rail qubits and four-level qudits.
