论文标题
在定向图上的两级量子步行者II：QRAM的应用
Two-level Quantum Walkers on Directed Graphs II: An Application to qRAM
论文作者
论文摘要
这是一系列两篇论文。使用两个内部状态的多粒子连续量子步行，这已在第一篇论文（Arxiv：2112.08119）中进行了配制，我们实际上实现了量子随机访问存储器（QRAM）。带有地址信息的数据被编码为量子步行者。步行者穿过完美的二进制树以访问指定的存储单元并复制存储在单元格中的数据。在每个节点分配的一个回旋门作为路由器，可以将步行者从父节点转移到两个子节点之一，这取决于沃克的内部状态。在此过程中，地址信息被顺序编码到内部状态，以便将步行者充分传递到目标单元。目前的QRAM处理$ 2^n $ $ m $ $ qubit数据，在深度$ o（n \ log（n+m））$的量子电路中实现，并且需要$ o（n+m）$ qubit Resources。这比需要$ o（n^2+nm）$ step和$ o（2^{n}+m）$ o（2^{n}+m）$ QUBIT资源来处理的传统存储桶QRAM更有效。此外，由于步行者没有与二进制树上的任何设备纠缠在一起，因此可以降低保持连贯性的成本。值得注意的是，通过简单地将量子步道通过二进制树，可以自动以量子叠加状态提取数据。换句话说，不需要任何时间依赖时间的控制。
This is the second paper in a series of two. Using a multi-particle continuous-time quantum walk with two internal states, which has been formulated in the first paper (arXiv:2112.08119), we physically implement a quantum random access memory (qRAM). Data with address information are dual-rail encoded into quantum walkers. The walkers pass through perfect binary trees to access the designated memory cells and copy the data stored in the cells. A roundabout gate allocated at each node serves as a router to move the walker from the parent node to one of two child nodes, depending on the internal state of the walker. In this process, the address information is sequentially encoded into the internal states so that the walkers are adequately delivered to the target cells. The present qRAM, which processes $2^n$ $m$-qubit data, is implemented in a quantum circuit of depth $O(n\log(n+m))$ and requires $O(n+m)$ qubit resources. This is more efficient than the conventional bucket-brigade qRAM that requires $O(n^2+nm)$ steps and $O(2^{n}+m)$ qubit resources for processing. Moreover, since the walkers are not entangled with any device on the binary trees, the cost of maintaining coherence can be reduced. Notably, by simply passing quantum walkers through binary trees, data can be automatically extracted in a quantum superposition state. In other words, any time-dependent control is not required.
