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

Abstract: High-fidelity quantum state transfer is critical for quantum communication and scalable quantum computation. Current quantum state transfer algorithms on the complete bipartite graph, which are based on discrete-time quantum walk search algorithms, suffer from low fidelity in some cases. To solve this problem, in this paper we propose a two-stage quantum state transfer algorithm on the complete bipartite graph. The algorithm is achieved by the generalized Grover walk with one marked vertex. The generalized Grover walk's coin operators and the query oracles are both parametric unitary matrices, which are designed flexibly based on the positions of the sender and receiver and the size of the complete bipartite graph. We prove that the fidelity of the algorithm 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 sender and receiver are in the same partition or different partitions of the complete bipartite graph. The algorithm provides a novel approach to achieve high-fidelity quantum state transfer on the complete bipartite graph in any case, which will offer potential applications for quantum information processing.