Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central prob...
Andrew M. Childs, Leonard J. Schulman, Umesh V. Va...
In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved effi...
We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on t...
We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether S is a semigroup or ...
: Can Grover’s algorithm speed up search of a physical region—for example a 2-D grid of size √ n × √ n? The problem is that √ n time seems to be needed for each query, j...