QnTM: Quantum Information Processing with Quantum Random Walks

我们对量子信息理解的最新进展表明，基于基本量子原理（如干涉和纠缠）的计算设备可以比任何经典计算机更快地执行某些计算任务。基于这些原理的计算设备的潜在分支已经激发了旨在确定这种设备的信息处理能力以及用于物理地实现它们的可能方法的大量努力。一个特别有前途的研究方向集中在量子随机行走（QRW）的发展上。这种基本的算法构建块是物理实现的一个特别有吸引力的候选者，因为它比通用量子计算复杂得多，并且仍然有有趣的算法应用。 我们将探索现实的物理系统，其中QRW可以实现，如超冷里德伯原子，并特别注意明确的实验问题，如激光激发序列和冗余检测，以允许错误拒绝。我们还将开发退相干的理论模型，特别关注退相干对QRW属性的影响，这些属性是当前算法应用的基础。 特别地，我们将研究不完美行走格的影响（也就是说，行走发生在一个不完美的组合结构上的情况，比如一个删除了一些节点的网格），无意的部分测量对QRW的影响，非均匀的站点-站点相互作用对QRW的影响，以及多个粒子的影响。我们描述了如何可以使用超冷原子系综来处理量子信息，并描述了一个新的方案的基础上，在光学晶格中的超冷里德伯原子实现连续时间QRW。拟议的研究涵盖了新的途径，例如由于不完美的行走晶格或无意的部分测量的影响，以及一种新形式的条件相互作用（货车德瓦尔斯封锁）准备量子比特和执行量子门的QRW中的退相干模型。更广泛的影响：拟议的活动将促进各级的教学和培训。此外，在国家和国际两级开展的充满活力的合作努力将加强思想和信息的交流，并通过交换学生和博士后研究人员促进培训。 拟议活动的多学科性质（研究、培训和推广）将使包括计算机科学、应用数学、电气工程和物理学在内的许多子领域相互促进。 最后，除了量子信息处理研究的直接影响之外，对多体量子比特的更深入理解将影响实现量子信息处理的新方案和研究的发展。

Recent advances in our understanding of quantum information suggest that computational devices based on fundamental quantum principles, such as interference and entanglement, could perform certain computational tasks much more quickly than any classical computer. The potential ramifications of computing devices based on these principles have inspired a great deal of effort aimed at determining the information processing power of such devices and possible methods for physically realizing them. A particularly promising direction of research has focused on the development of the quantum random walk (QRW). This basic algorithmic building-block is an especially attractive candidate for physical realization, as it is significantly less complex than general-purpose quantum computation and still has interesting algorithmic applications.We shall study QRWs, focusing both on implementation and theoretical issues. We will explore realistic physical systems in which QRWs could be realized, such as ultracold Rydberg atoms, and pay special attention to explicit experimental issues, such as laser excitation sequences and redundant detection to allow error rejection. We will also develop theoretical models of decoherence, specifically focusing on the effect that decoherence has on the properties of QRWs that underly current algorithmic applications. In particular, we will study the effect of imperfect walk lattices (that is, the situation where the walk takes place on an imperfect combinatorial structure, like a grid with some nodes removed), the effect of unintentional partial measurement on QRWs, the effect of non-uniform site-site interaction on QRW, and the effect of multiple particles.Intellectual Merit: We describe how ensembles of ultracold atoms can be used to process quantum information, and describe a new scheme based on ultracold Rydberg atoms in optical lattices to implement a continuous-time QRW. The proposed research covers new avenues, such as models of decoherence in QRWs due to imperfect walk lattices or effect of unintentional partial measurements, and a novel form of conditional interaction (the van der Waals blockade) to prepare qubits and execute quantum gates. Broader Impact: The proposed activities will promote teaching and training at all levels. In addition, the vibrant collaborative efforts, at the national and international levels, will enhance the flow of ideas and information, as well as promote training via exchange of students and postdoctoral researchers. The multidisciplinary nature of the proposed activities (research, training, and outreach) will cross-fertilize numerous subfields including computer science, applied mathematics, electrical engineering, and physics. Finally, beyond the immediate impact of the proposed research in quantum information processing, a deeper understanding of many-body qubits will impact development of new schemes and studies to implement quantum information processing.