2021/09/26 by Jaideep Mulherkar, Mulherkar, Jaideep, Rishikant Rajdeepak +3
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #FOS: Physical sciences #Mathematics #Parallel computing #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #State (computer science) #Transfer (computing) #quant-ph
paper · pdf · doi:10.48550/arxiv.2109.12607
arxiv created 2021/09/26 · openalex publication_date 2021/09/26 · arxiv updated 2021/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk is governed by the unitary operator U(t) = eiAt, where A is the adjacency matrix of the graph. An important notion in the quantum random walk is the transfer of a quantum state from one vertex to another. If the fidelity of the transfer is unity, we call it a perfect state transfer. Many graph families have been shown to admit PST or periodicity, including cubelike graphs. These graphs are unweighted. In this paper, we generalize the PST or periodicity of cubelike graphs to that of weighted cubelike graphs. We characterize the weights for which they admit PST or show periodicity, both at time t=\fracπ2.