Continuous-time quantum random walks require discrete space

Kia Manouchehri, Jingbo Wang

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.
Original languageEnglish
Pages (from-to)13773-13785
JournalJournal of Physics A: Mathematical and Theoretical
Issue number45
Publication statusPublished - 2007


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