Quantum-walk-based state-transfer algorithms on the complete <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>M</mml:mi></mml:math> -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 vertex, algorithm finds marked vertex unit probability limit of large graph. Next, we employ evolution operator two perform state transfer between sender receiver. show when receiver are different partitions, succeeds fidelity approaching unity for However, same partition, does not reach exactly 1. To solve this problem, propose an active switch, whose can be estimated based single alone.