Quantum walks: linear algebra, graphs, and quantum computing
The interplay between the properties of graphs and the eigenvalues of their adjacency matrices is well-known. Important graph invariants,such as diameter and chromatic number, can be understood using eigenvalue techniques. In this talk, we bring these classical techniques in algebraic graph theory to the study of quantum walks.
A system of interacting quantum qubits can be modelled by a quantum process on an underlying graph and is, in some sense, a quantum analogue of random walk. This gives rise to a rich connection between graph theory, linear algebra and quantum computing. In this talk, I will give an introduction to this area, as well as various recent results.
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