Physics – Quantum Physics
Scientific paper
2006-11-05
STOC 2007
Physics
Quantum Physics
29 pages, v2: added automorphism principle, extended to non-boolean functions, simplified examples, added matching upper bound
Scientific paper
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower bounds, and is versatile with equivalent formulations in terms of weight schemes, eigenvalues, and Kolmogorov complexity. All these formulations rely on the principle that if an algorithm successfully computes a function then, in particular, it is able to distinguish between inputs which map to different values. We present a stronger version of the adversary method which goes beyond this principle to make explicit use of the stronger condition that the algorithm actually computes the function. This new method, which we call ADV+-, has all the advantages of the old: it is a lower bound on bounded-error quantum query complexity, its square is a lower bound on formula size, and it behaves well with respect to function composition. Moreover ADV+- is always at least as large as the adversary method ADV, and we show an example of a monotone function for which ADV+-(f)=Omega(ADV(f)^1.098). We also give examples showing that ADV+- does not face limitations of ADV like the certificate complexity barrier and the property testing barrier.
Hoyer Peter
Lee Taegweon
Spalek Robert
No associations
LandOfFree
Negative weights make adversaries stronger does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Negative weights make adversaries stronger, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Negative weights make adversaries stronger will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-595040