QnTM: Quantum Information Processing with Quantum Random Walks

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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.