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Lecture 1 - Quantum walk and learning graph based algorithms (a tutorial)

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Mathematical Challenges in Quantum Information

In this talk I survey two generic methods to design quantum algorithms. I give an intuitive treatment of the discrete time quantization of classical Markov chains, and I describe nested walks, an extension of the model using quantum data structures. I explain the relatively recent idea of learning graphs, a combinatorial way to conceive quantum query algorithms. With several examples, including triangle and 3-collision finding, I illustrate the power of these methods. Finally I discuss time efficient implementations of learning graphs by quantum walks.

This talk is part of the Isaac Newton Institute Seminar Series series.

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