An effective Hamiltonian approach to quantum random walk

@article{Sarkar2015AnEH,
  title={An effective Hamiltonian approach to quantum random walk},
  author={Debajyoti Sarkar and Niladri Paul and Kaushik Bhattacharya and Tarun Kanti Ghosh},
  journal={Pramana},
  year={2015},
  volume={88},
  pages={1-14}
}
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed… 
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4 Citations
Background Citations
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4 Citations

The Dirac equation as a quantum walk over the honeycomb and triangular lattices
TLDR
It is shown that the Dirac equation in $(2+1)$ dimensions can be simulated, through local unitaries, on the honeycomb or the triangular lattice, both of interest in the study of quantum propagation on the nonrectangular grids, as in graphene-like materials.
Construction of distinct discrete time scattering quantum walk formulations on the honeycomb lattice
Quantum walks : background geometry and gauge invariance
Les denommees marches quantiques, evolutions quantiques locales sur graphes discrets, sont un outil tres pratique pour simuler certains systemes physiques. Nous nous limiterons a leur version a temps…
Landau levels for discrete-time quantum walks in artificial magnetic fields

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