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From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We… (More)

Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson localisation. Here, we consider a directed discrete-time quantum walk as a model to study quantum percolation of a… (More)

Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular… (More)

Long-time limit distributions are key quantities for understanding the asymptotic dynamics of quantum walks, and they are known for most forms of one-dimensional quantum walks using two-state coin systems. For two-dimensional quantum walks using a four-state coin system, however, the only known limit distribution is for a walk using a parameterized Grover… (More)

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