Discrete-time quantum walk and its Hamiltonian form in different lattices along with temporal, spatial, and fluctuating disordered operation

Details Discrete-time quantum walk and its Hamiltonian form in different lattices along with temporal, spatial, and fluctuating disordered operation Discrete-time quantum walk and its Hamiltonian form in different lattices along with temporal, spatial, and fluctuating disordered operation

2011-03-14

arxiv.org/abs/1103.2704v3

Physics

Quantum Physics

11 pages, 8 figures, revised and extended version with 4 new figures

Scientific paper

Quantum walks and its dynamic properties have provided a framework to various applications ranging from quantum computing to simulation of physical processes. The standard discrete-time quantum walk evolution is described using a quantum coin operation followed by a shift operation. Starting from a standard description, we present an Hamiltonian form of the operator for each step of the discrete-time quantum walk evolution on a line using two-state particle. We extend the description for a walk evolution on some of the two- and three-dimensional lattice structures such as, square, triangular, kagome, honeycomb, and cubic lattices using two-state particle and different Pauli basis for each axis. We also describe the walk dynamics using temporal, spatially static, and fluctuating disordered unitary evolutions in one dimension and show that the localization is possible only with a spatially static disordered operations. This provides a general framework to simulate, control, and study the dynamics in form of ordered and disordered Hamiltonian operations in various one- and two-dimensional systems.

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