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arXiv · 0902.3496

Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs

Domenico D'Alessandro
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Abstract

I obtain the dynamics of the continuous time quantum walk on a $d$-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main result of arXiv:quant-ph/0606050 which proved this limit for the infinite line. By highlighting the main features of the limiting procedure, I then extend it to general graphs. For a given discrete time quantum walk on a general graph, I single out the type of continuous dynamics (Hamiltonians) that can be obtained as a limit of the discrete time dynamics.

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Domenico D'Alessandro. 2009-02-20. Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs. https://doi.org/10.1016/s0034-4877(10)80025-4

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