Quantum state transfer on the complete bipartite graph

TL;DR

This paper extends quantum state transfer techniques on complete bipartite graphs, demonstrating high-fidelity transfer with varied partition sizes and introducing an active switch method using lackadaisical quantum walks.

Contribution

It generalizes previous results by enabling state transfer between differently sized partitions and proposes an active switching approach with lackadaisical quantum walks.

Findings

High-fidelity state transfer with different partition sizes

Active switch approach using lackadaisical quantum walks

Extension of previous perfect transfer conditions

Abstract

Previously it was shown that (almost) perfect state transfer can be achieved on the complete bipartite graph by a discrete-time coined quantum walk based algorithm when both the sender and receiver vertices are in the same partition of the graph and when the sender and receiver are in opposite partitions of the same size. By changing the coin operator, we analyze the state transfer problem and we show that it is still possible to achieve state transfer with high fidelity even when the sender and receiver are in different partitions with different sizes. Moreover, it is also possible to use an active switch approach using lackadaisical quantum walks where the marked vertex is switched between the sender and receiver during the algorithm.