TY - JOUR T1 - Quantum Adversary (Upper) Bound JF - Chicago Journal of Theoretical Computer Science Y1 - 2013 A1 - Shelby Kimmel AB - We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity without producing an algorithm. For example, we describe an oracle problem which we prove (non-constructively) can be solved in $O(1)$ queries, where the previous best quantum algorithm uses a polylogarithmic number of queries. We then give an explicit $O(1)$-query algorithm for this problem based on span programs. VL - 19 U4 - 1 - 14 UR - http://arxiv.org/abs/1101.0797v5 CP - 1 J1 - Chicago J. of Theoretical Comp. Sci. U5 - 10.4086/cjtcs.2013.004 ER -