Quantum Implications of Huang's Sensitivity Theorem
Electronic Colloquium on Computational Complexity, pp. 662020.
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 (...More
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