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arXiv · 1501.04396

Perfect state transfer in products and covers of graphs

Gabriel Coutinho·Chris Godsil
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Abstract

A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits, transfer of state among such qubits throughout time can be formalized as the action of the continuous-time quantum walk operator in the characteristic vectors of the vertices. Here we are concerned with the problem of determining which graphs admit a perfect transfer of state. More specifically, we will study graphs whose adjacency matrix is a sum of tensor products of $01$-matrices, focusing on the case where a graph is the tensor product of two other graphs. As a result, we will construct many new examples of perfect state transfer.

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Gabriel Coutinho, Chris Godsil. 2015-01-19. Perfect state transfer in products and covers of graphs. https://doi.org/10.1080/03081087.2015.1033381

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