Introduction to Quantum Random Walks

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This course aims to provide an introduction to the recent subject of Quantum Random Walk. The lectures will cover:

Main topics

Review of classical random walks

• Simple random walks
• Markov chains
• Random wlaks on graphs
• Ergodicity, mixing anc convergence properties
• Extensions to the continuum, diffusion processes

Quantum Random Walks

• From Feynman’s derivation to the definition of simple quantum walks
• Dicrete-time walks on graphs, mixing properties,hitting times
• Walks on d-dimensional lattices and continuum limits
• Quantum walks in continous-time
• Path integral formulation, Fourier approach, convergence properties at infinite times
• Applications to quantum computation, quantum algorithms and cellular automata