2022/07/04 by Qiuting Chen, Chris Godsil, Chen, Qiuting +5 · 3 citations
Computer Science · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2207.01673
openalex publication_date 2022/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like arc-reversal walks, vertex-face walks. For the transition matrix of a quantum walk, there is a Hamiltonian associated with it. We will study the Hamiltonians of the bipartite walks. Let S be a skew-symmetric matrix. We are mainly interested in the Hamiltonians of the form iS. We show that the Hamiltonian can be written as iS if and only if the adjacency matrix of the bipartite graph is invertible. We show that arc-reversal walks and vertex-face walks are special cases of bipartite walks. Via the Hamiltonians, phenomena of bipartite walks lead to phenomena of continuous walks. We show in detail how we use bipartite walks on paths to construct universal perfect state transfer in continuous walks.