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High-fidelity quantum state transfer is critical for quantum communicationand scalable quantum computation. Current quantum state transfer algorithms onthe complete bipartite graph, which are based on discrete-time quantum walksearch algorithms, suffer from low fidelity in some cases. To solve thisproblem, in this paper we propose a two-stage quantum state transfer algorithmon the complete bipartite graph. The algorithm is achieved by the generalizedGrover walk with one marked vertex. The generalized Grover walk's coinoperators and the query oracles are both parametric unitary matrices, which aredesigned flexibly based on the positions of the sender and receiver and thesize of the complete bipartite graph. We prove that the fidelity of thealgorithm is greater than$1-2\epsilon_{1}-\epsilon_{2}-2\sqrt{2}\sqrt{\epsilon_{1}\epsilon_{2}}$ or$1-(2+2\sqrt{2})\epsilon_{1}-\epsilon_{2}-(2+2\sqrt{2})\sqrt{\epsilon_{1}\epsilon_{2}}$for any adjustable parameters $\epsilon_{1}$ and $\epsilon_{2}$ when the senderand receiver are in the same partition or different partitions of the completebipartite graph. The algorithm provides a novel approach to achievehigh-fidelity quantum state transfer on the complete bipartite graph in anycase, which will offer potential applications for quantum informationprocessing.

A high-fidelity quantum state transfer algorithm on the complete bipartite graph