Connecting the discrete- and continuous-time quantum walks

By Frederick W. Strauch. 2006

164 citations recorded by the source corpus.

Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time quantum walk. Though the properties of these two walks have shown similarities, it has remained an open problem to find the exact relation between the two. The precise connection of these two processes, both quantally and classically, is presented. Extension to higher dimensions is also discussed.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e398a2d47d18096dbb0b16c14d44492bfa9f9817

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Citations in the corpus

Quantum walks: a comprehensive review (2012, methodology): “8), the additional stimulus provided by [424] as well as the computational universality of quantum walks [113,301,436] and recent connections found between quantum walks and adiabatic quantum computation [106], another model of continuous quantum computation, it is reasonable to expect new implement”
Universal quantum computation using the discrete-time quantum walk (2009, background): “ete time walks. Strauch has shown that, as we take the continuous limit of the discrete time walk on the line, we actually get two copies of the continuous time walk propagatingin opposite directions [18]. Childs later showed a direct correspondence between the discrete and continuous time quantum w”
On the Relationship Between Continuous- and Discrete-Time Quantum Walk (2008, methodology): “Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.”