2019/05/31 by Balázs Endre Szigeti, Gábor Homa, Zoltán Zimborás +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Discrete mathematics #Exponent #Graph #Mathematics #Network topology #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum mechanics #Quantum walk #Statistical physics #Time evolution #Topology (electrical circuits) #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreva.100.062320
published as Phys. Rev. A 100, 062320 (2019) · 12 pages, 5 figures; v2: typos corrected, references added
arxiv created 2019/06/13 · openalex publication_date 2019/12/16 · arxiv updated 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Dynamical evolution of systems with sparse Hamiltonians can always be recognized as continuous-time quantum walks (CTQWs) on graphs. In this paper, we analyze the short-time asymptotics of CTQWs. In recent studies, it was shown that for the classical diffusion process the short-time asymptotics of the transition probabilities follows power laws whose exponents are given by the usual combinatorial distances of the nodes. Inspired by this result, we perform a similar analysis for CTQWs in both closed and open systems, including time-dependent couplings. For time-reversal symmetric coherent quantum evolutions, the short-time asymptotics of the transition probabilities is completely determined by the topology of the underlying graph analogously to the classical case, but with a doubled power-law exponent. Moreover, this result is robust against the introduction of on-site potential terms. However, we show that time-reversal symmetry-breaking terms and noncoherent effects can significantly alter the short-time asymptotics. The analytical formulas are checked against numerics, and excellent agreement is found. Furthermore, we discuss in detail the relevance of our results for quantum evolutions on particular network topologies.