39,798 research outputs found
Optimal computation with non-unitary quantum walks
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times, respectively. Non-unitary quantum walks can provide a useful optimisation of these properties, producing a more uniform distribution on the line, and faster mixing times on the cycle. We investigate the interplay between quantum and random dynamics by comparing the resources required, and examining numerically how the level of quantum correlations varies during the walk. We show numerically that the optimal non-unitary quantum walk proceeds such that the quantum correlations are nearly all removed at the point of the final measurement. This requires only O(logT) random bits for a quantum walk of T steps
Large Deviations for processes on half-line
We consider a sequence of processes defined on half-line for all non negative
t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in
the space of continuous functions with a new metric that is more sensitive to
behaviour at infinity than the uniform metric. LDP is established for Random
Walks, Diffusions, and CEV model of ruin, all defined on the half-line. LDP in
this space is "more precise" than that with the usual metric of uniform
convergence on compacts.Comment: 23 page
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