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Decoherence in Quantum Walks on the Hypercube

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arxiv quant-ph/0501169 v5 pith:DNHCCUCM submitted 2005-01-28 quant-ph

Gorjan Alagic , Alexander Russell This is my paper · ORCID
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keywords decoherencequantumwalkshypercubeprovethresholdbehavebeneath
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We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that in this model there is a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing times, are preserved. Beyond the threshold, we prove that the walks behave like their classical counterparts.

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  1. Quantum algorithm for estimating volumes of convex bodies

    quant-ph 2019-08 accept novelty 8.0 of 10

    A quantum algorithm estimates the volume of an n-dimensional convex body within error epsilon using O-tilde(n^3 + n^2.5/epsilon) membership queries, the first quantum speedup for this task.

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