Physical Implementation of Quantum Random Walks

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Quantum random walks have received much interest due to their non-
intuitive dynamics, which may hold a key to radically new quantum
algorithms. What remains a major challenge is a physical realization
that is experimentally viable, readily scalable, and not limited to
specific connectivity criteria. In this seminar, I will present an
implementation scheme for quantum walking on arbitrarily complex
graphs. This scheme is particularly elegant since the walker is not
required to physically step between the nodes; only flipping coins is
sufficient. In addition, by taking advantage of the inherent structure
of the CS decomposition of unitary matrices, we are able to implement
all coin operations necessary for each step of the walk simultaneously. This scheme can be physically realized using a variety of quantum systems, such as cold atoms trapped inside an optical lattice or electrons inside coupled quantum dots.