An effective Hamiltonian approach to quantum random walk

  title={An effective Hamiltonian approach to quantum random walk},
  author={Debajyoti Sarkar and Niladri Paul and Kaushik Bhattacharya and Tarun Kanti Ghosh},
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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