Quantum Implications of Huang's Sensitivity Theorem
Abstract
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, the deterministic query complexity, $D(f)$, is at most quartic in the quantum query complexity, $Q(f)$: $D(f) = O(Q(f)^4)$. This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, Santha, and Smotrovs (2017). We also use the result to resolve the quantum analogue of the AanderaaKarpRosenberg conjecture. We show that if $f$ is a nontrivial monotone graph property of an $n$vertex graph specified by its adjacency matrix, then $Q(f) = \Omega(n)$, which is also optimal.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.13231
 Bibcode:
 2020arXiv200413231A
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity