We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pa...
: The theoretical study of quantum computation has yielded efficient algorithms for some traditionally hard problems. Correspondingly, experimental work on the underlying physical...
Steven Balensiefer, Lucas Kreger-Stickles, Mark Os...
We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is a solution to the Unique Shortest Vector Problem (SVP) under ...
In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s...
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...