Connection Between Continuous and Discrete Time Quantum Walks on d-Dimensional Lattices; Extensions to General Graphs
arXiv:0902.3496 · doi:10.1016/S0034-4877(10)80025-4
Abstract
I obtain the dynamics of the continuous time quantum walk on a -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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Cited by in corpus (9)
- Crossovers induced by discrete-time quantum walks
- Continuous Limit of Discrete Quantum Walks
- Continuous-time quantum walks on planar lattices and the role of the magnetic field
- Discrete-time quantum walks as fermions of lattice gauge theory
- The Heun differential equation and the Gauss differential equation related to quantum walks
- Steepest Entropy Ascent Solution for a Continuous-Time Quantum Walker
- Controllability of Quantum Walks on Graphs
- Exact simulation of coined quantum walks with the continuous-time model
- Perturbed graphs achieve unit transport efficiency without environmental noise