ECCC-Report TR20-066https://eccc.weizmann.ac.il/report/2020/066Comments and Revisions published for TR20-066en-usSun, 03 May 2020 14:01:55 +0300
Paper TR20-066
| Quantum Implications of Huang's Sensitivity Theorem |
Scott Aaronson,
Shalev Ben-David,
Robin Kothari,
Avishay Tal
https://eccc.weizmann.ac.il/report/2020/066Based 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 Aanderaa-Karp-Rosenberg 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.Sun, 03 May 2020 14:01:55 +0300https://eccc.weizmann.ac.il/report/2020/066