# Quantum Walk Sampling by Growing Seed Sets

@inproceedings{Apers2019QuantumWS, title={Quantum Walk Sampling by Growing Seed Sets}, author={Simon Apers}, booktitle={ESA}, year={2019} }

This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as $\widetilde{O}(m^{1/3} \delta^{-1/3})$, with $m$ the number of edges and $\delta$ the random walk spectral gap. This improves on existing strategies by initially growing a classical seed set in the graph, from which a quantum walk is then run. The algorithm leads to a… CONTINUE READING

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