Quantum Random Walks with position-dependent parameters
Jędrzej Stempin

Date, Time
14.03, 15:00 - 16:00

Quantum Random Walks are considered as a toy model for simulations of complicated physical systems, namely – the solutions of the Dirac equation. To emphasize possible applications, the model can be discussed in the context of Classical Random Walks which are widely used in searching algorithms. It turns out that the Quantum Random Walks outperform their classical counterparts as far as the speed of propagation is concerned. The wave function occurs to spread even faster if the dependency of the parameters on position is incorporated. Motivated by this fact we carry out the analysis of the Quantum Random Walks with position dependent parameters by examining symmetries acquired by the evolution operator. Moreover, the framework for analysis is presented, especially discrete Wigner functions and the decoherence mechanisms leading to the exposition of the relationship between Quantum and Classical Random Walks.