Staggered Quantum Walks With Superconducting Microwave Resonators

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The staggered quantum walk is a model defined by the product of local operators associated with two or more independent graph tessellations. This model is versatile, encompasses several well-known discrete-time quantum walks, and inherits interesting features of the continuous-time quantum walk. We propose an implementation of the staggered quantum walk model with superconducting microwave resonators, where the required local operations are provided by the nearest neighbor interaction of the resonators coupled through superconducting quantum interference devices. The tunability of the interactions makes this system an excellent toolbox for this class of quantum walks. We focus on the one-dimensional case and discuss its generalization to a more general class known as triangle-free graphs.9514CNPq [PDJ 165941/2014-6, 303406/2015-1, 474143/2013-9]FAPESP through the Research Center in Optics and Photonics (CePOF)Faperj [26/102.350/2013]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Coined Quantum Walks as Quantum Markov Chains

We analyze the equivalence between discrete-time coined quantum walks and Szegedy's quantum walks. We characterize a class of flip-flop coined models with generalized Grover coin on a graph $\Gamma$ that can be directly converted into Szegedy's model on the subdivision graph of $\Gamma$ and we describe a method to convert one model into the other. This method improves previous results in literature that need to use the staggered model and the concept of line graph, which are avoided here.Comment: 10 pages, 4 fig