Non-reversal open quantum walks.
Goolam Hoosen, Yashine Hazmatally.
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In this thesis, a new model of non-reversal quantum walk is proposed. In such a walk, the walker cannot go back to previously visited sites but it can stay static or move to a new site. The process is set up on a line using the formalism of Open Quantum Walks (OQWs). Afterwards, non-reversal quantum trajectories are launched on a 2-D lattice to which a memory is associated to record visited sites. The “quantum coins” are procured from a randomly generated unitary matrix. The radius of spread of the non-reversal OQW varies with di↵erent unitary matrices. The statistical results have meaningful interpretations in polymer physics. The number of steps of the trajectories is equivalent to the degree of polymerization, N. The root-mean-square of the radii determines the end-to-end distance, R of a polymer. These two values being typically related by R ⇠ N⌫, the critical exponent, ⌫, is obtained for N 400. It is found to be closely equal to the Flory exponent. However, for larger N, the relationship does not hold anymore. Hence, a di↵erent relationship between R and N is suggested.