发表机构
University of Rochester; Max Planck Institute for the Physics of Complex Systems（罗切斯特大学; 马克斯·普朗克复杂系统物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用d正则无向连通简单图及从哈尔测度均匀分布抽取的酉硬币算子构建离散量子随机游走变体，分析其性质及在阿贝尔群凯莱图上的示例，虽硬币子空间去极化，但顶点子空间测量可揭示初始态信息。
AI 中文摘要
我们使用从关于哈尔测度的均匀分布中抽取的酉硬币算子，利用d正则无向连通简单图构造离散量子随机游走的一个变体。每次游走步骤，硬币算子随机矩阵独立抽取。相关量子通道随机酉分布的期望值给出硬币子空间的去极化通道，类似于经典随机游走。尽管平均通道使硬币子空间去极化，但顶点子空间测量可设计来揭示初始量子态信息。我们用阿贝尔群凯莱图上的量子游走示例说明，如循环图和超立方体图。这些量子游走是二分强相互作用系统的示例，其中一个子系统受到强烈扰动，但另一个子系统中关于初始态的信息可能永远可测量。由于其退相干，具有哈尔随机硬币的量子随机游走在搜索算法中无用，但有助于理解具有强烈扰动子系统的量子系统。
英文摘要
With unitary coin operator that is a random matrix drawn from a uniform distribution with respect to the Haar measure, we construct a variant of a discrete quantum random walk using a d-regular undirected connected simple graph. With each step of the walk, the coin operator random matrix is drawn independently from the distribution. The expectation value over the distribution of random unitaries for the associated quantum channel gives a depolarization channel for the coin subspace and resembles the associated classical random walk where the direction a walker steps depends upon the outcome of a fair coin or balanced d-sided dice. Remarkably, despite the fact that the averaged channel depolarizes the coin subspace, measurements in the vertex subspace can be designed that would reveal information about the initial quantum state, even after many iterations of the channel. We illustrate with examples of quantum walks on Cayley graphs of Abelian groups, such as the cycle and hypercube graphs. For Cayley graphs of Abelian groups, the averaged channel is dephasing in the Fourier basis. These quantum walks are examples of bipartite strongly interacting systems, where one subsystem is strongly perturbed, yet information about the initial state in the other subsystem is potentially measurable forever. Due to its decoherence, a quantum random walk with a Haar-random coin would not be useful in search algorithms but could aid in understanding quantum systems with strongly perturbed subsystems.
