Abstract. We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be a...
The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bo...
We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our resu...
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical "black box" function drawn from some set of such bl...
We obtain the strongest separation between quantum and classical query complexity known to date--specifically, we define a black-box problem that requires exponentially many querie...