2023/08/26 by Bikash Bhattacharjya, Bhattacharjya, Bikash, Hermie Monterde +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #05C50 #05C76 #15A16 #15A18 #81P45 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Molecular Junctions and Nanostructures #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena
paper · pdf · doi:10.48550/arxiv.2308.13887
openalex publication_date 2023/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A blow-up of n copies of a graph G is the graph \oversetn\uplus~G obtained by replacing every vertex of G by an independent set of size n, where the copies of vertices in G are adjacent in the blow-up if and only if the vertices adjacent in G. Our goal is to investigate the existence of quantum state transfer on a blow-up graph \oversetn\uplus~G, where the adjacency matrix is taken to be the time-independent Hamiltonian of the quantum system represented by \oversetn\uplus~G. In particular, we establish necessary and sufficient conditions for vertices in a blow-up graph to exhibit strong cospectrality and various types of high probability quantum transport, such as periodicity, perfect state transfer (PST) and pretty good state transfer (PGST). It turns out, if \oversetn\uplus~G admits PST or PGST, then one must have n=2. Moreover, if G has an invertible adjacency matrix, then we show that every vertex in \overset2\uplus~G pairs up with a unique vertex to exhibit strong cospectrality. We then apply our results to determine infinite families of graphs whose blow-ups admit PST and PGST.