Quantum Random Walk onTwo Dimensional Lattice with Two-State Particle

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Hasani, Majid | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45218 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Karimipour, Vahid
Abstract:
Quantum random walk is a computational model in quantum computation which is as powerful as other models like quantum circuit model. One dimensional random walks can be implemented in the laboratory by using a two-level quantum coin (e.g. the two states of a photon). For implementing higher dimensional random walks, one should simulate quantum coins with higher number of levels. This is difficult to implement experimentally. Various proposals try to bypass this problem, like the proposal of alternate walks in [C. DiFranco et al., Phys. Rev. Lett. 106, 080502(2011)]. Here we suggest an alternate solution: We use the bi-partite structure of some lattices to effectively act as a two-level intrinsic coin, leaving the other two levels to be implemented by an ordinary quantum coin (a photon)
Keywords:
Ladder System ; Discrete Time Quantum Random Walk ; Conditional Translational Operator ; Coin Operator ; Hexagonal Lattice ; Grover Algorithm