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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Quantum Property Testing for Bounded-Degree Graphs
verfasst von : Andris Ambainis, Andrew M. Childs, Yi-Kai Liu
Erschienen in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Verlag: Springer Berlin Heidelberg
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We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time
$\tilde O(N^{1/3})$
, beating the
$\Omega(\sqrt{N})$
classical lower bound. For testing expansion, we also prove an
$\tilde\Omega(N^{1/4})$
quantum query lower bound, thus ruling out the possibility of an exponential quantum speedup. Our quantum algorithms follow from a combination of classical property testing techniques due to Goldreich and Ron, derandomization, and the quantum algorithm for element distinctness. The quantum lower bound is obtained by the polynomial method, using novel algebraic techniques and combinatorial analysis to accommodate the graph structure.