2008/01/01 by Diego de Falco, Dario Tamascelli
Computer Science · Materials Science · Physics and Astronomy · #Chemical and Physical Properties of Materials #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #quant-ph
paper · pdf · doi:10.1007/978-3-540-77566-9_45
published as V. Geffert et al. (Eds.): SOFSEM 2008, LNCS 4910, pp. 519-530, 2008 · 12 pages, 3 figures
openalex publication_date 2008/01/01 · arxiv created 2008/01/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus, propagates at a rate which is linear in time, as compared to the square root rate for a classical random walk. Indeed, it has been suggested that there are graphs that can be traversed by a quantum walker exponentially faster than by the classical random analogue. In this note we adopt the approach of exploring the conditions to impose on a Markov process in order to emulate its quantum counterpart: the central issue that emerges is the problem of taking into account, in the numerical generation of each sample path, the causative effect of the ensemble of trajectories to which it belongs. How to deal numerically with this problem is shown in a paradigmatic example.