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Perfect state transfer can be achieved between two marked vertices of graphs like a star graph, a complete graph with self-loops and a complete bipartite graph, and two-dimensional Lattice by means of discrete-time quantum walk. In this paper, we investigate the quality of quantum state transfer between two marked vertices of an unsymmetrical graph like the butterfly network. Our numerical results support the conjecture that the fidelity of state transfer depends on the quantum state to be transferred dynamically. The butterfly network is a typical example studied in networking coding. Therefore, these results can provide a clue to the construction of quantum network coding schemes.

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