01146nas a2200145 4500008004100000245005500041210005400096260001500150300001200165520072600177100002100903700002300924700001600947856003700963 2010 eng d00aQuantum property testing for bounded-degree graphs0 aQuantum property testing for boundeddegree graphs c2010/12/14 a365-3763 a We study quantum algorithms for testing bipartiteness and expansion of
bounded-degree graphs. We give quantum algorithms that solve these problems in
time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing
expansion, we also prove an 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.
1 aAmbainis, Andris1 aChilds, Andrew, M.1 aLiu, Yi-Kai uhttp://arxiv.org/abs/1012.3174v3