Sophie Laplante

We prove a very general lower bound technique for quantum and randomized query complexity that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique generalizes the weighted, unweighted methods of Ambainis, and the spectral method of Barnum, Saks, and Szegedy. As an immediate consequence of our main theorem, adversary methods can only prove lower bounds for Boolean functions f in O(min(sqrt{n C0(f)}, sqrt{n C1(f)})), where C0, C1 is the certificate complexity, and n is the size of the input. We also derive a general form of the ad hoc weighted method used by Hoyer, Neerbek, and Shi to give a quantum lower bound on ordered search and sorting. Reference: quant-ph/0311189 (This is joint work with Frederic Magniez.)