Unitary coined discrete-time quantum walks on directed multigraphs

Unitary coined discrete-time quantum walks (UCDTQW) constitute a universal model of computation, meaning that any computation done by general purpose computer can either be using the UCDTQW framework. In last decades, great progress has been made in this field developing walk-based algorithms outperform classical ones. However, current computers work based on circuit and mapping from one to other is still an open problem. work, we provide matrix analysis unitary evolution operator UCDTQW, which composed at time shift coin operators. We conceive system as form adjacency associated with graph takes place, set equations transform latter into former vice versa. modifies structure original directed multigraph, splitting single edges arcs multiple arcs. Thus, fact representation means complies transformation will automatically circuit, acting bipartite always multigraph. Finally, extend definition superposition coins such way each acts different vertices multigraph description how implemented form.