Quantum-walk-based state-transfer algorithms on the complete M-partite graph

We investigate coined quantum-walk search and state-transfer algorithms, focusing on the complete M-partite graph with N vertices in each partition. First, it is shown that by adding a loop to each vertex, the search algorithm finds the marked vertex with unit probability in the limit of a large graph. Next, we employ the evolution operator of the search with two marked vertices to perform a state transfer between the sender and the receiver. We show that when the sender and the receiver are in different partitions, the algorithm succeeds with fidelity approaching unity for a large graph. However, when the sender and the receiver are in the same partition, the fidelity does not reach exactly 1. To solve this problem, we propose a state-transfer algorithm with an active switch, whose fidelity can be estimated based on the single vertex search alone.

Automated summary

The study focuses on the coined quantum-walk search and state-transfer algorithms, showing that marked vertices can be found with high probability in large graphs and successful state transfer between different partitions. However, when the sender and receiver are in the same partition, the fidelity does not reach exactly 1, leading to the proposal of a state-transfer algorithm with an active switch to address this issue.