Quantum property testing for bounded-degree graphs

Details Quantum property testing for bounded-degree graphs Quantum property testing for bounded-degree graphs

2010-12-14

arxiv.org/abs/1012.3174v3

Proceedings of RANDOM 2011, Lecture Notes in Computer Science 6845, pp. 365-376

Physics

Quantum Physics

21 pages; v3: more detailed proof of the lower bound; v2: minor corrections to Lemma 6

Scientific paper

10.1007/978-3-642-22935-0_31

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.

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