2025/08/01 by Hartosh Singh Bal, Bal, Hartosh Singh
Computer Science · Physics and Astronomy · #05C75 #05C90 #81P45 #81Q35 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #Spectroscopy and Quantum Chemical Studies #es: 05C50 (Primary)
paper · pdf · doi:10.48550/arxiv.2508.00562
openalex publication_date 2025/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study quantum coherence in continuous-time quantum walks on perfect graphs generated by the symmetric lift HL'2(G), a canonical, unweighted, undirected construction defined as the line graph of a bipartite double cover of G. This lift acts as both a coherence-preserving and coherence-inducing transformation: it preserves and scales structured quantum interference in highly symmetric base graphs, and induces sustained coherence in random or weakly structured ones. In small graphs such as K4, K5, and the Petersen graph, where quantum walks exhibit sharp revivals and high return probability, repeated HL'2 lifting produces towers of perfect graphs with thousands to tens of thousands of vertices that retain periodic or quasi-periodic coherence. When applied to random regular or Erdős--Rényi graphs with flat or decaying return behavior, the lift introduces structured interference and significant amplification of mean and peak return probabilities. To quantify these effects, we evaluate standard coherence metrics from quantum resource theory, including inverse participation ratio (IPR), purity, relative entropy of coherence, and the logarithmic coherence number. These measures confirm that HL'2 lifting delocalizes eigenstates, increases coherence entropy, and expands the basis support of quantum states. These results demonstrate that HL'2 is a scalable and structurally grounded mechanism for organizing quantum interference, and introduce a new family of perfect graphs that support long-time quantum coherence without spectral tuning or engineered weights.