TY - JOUR T1 - Quantum property testing for bounded-degree graphs JF - Proc. RANDOM Y1 - 2010 A1 - Andris Ambainis A1 - Andrew M. Childs A1 - Yi-Kai Liu AB - 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. U4 - 365-376 UR - http://arxiv.org/abs/1012.3174v3 J1 - Proceedings of RANDOM 2011 U5 - 10.1007/978-3-642-22935-0_31 ER -