We present two general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Both methods are based on the adversary method of Ambainis. We sh...
Abstract: We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of the adversary method, by analyzing the eigenspace structur...
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input,...
We introduce two new complexity measures for Boolean functions, which we name sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query com...
The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hype...