Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Implications of Huang's Sensitivity Theorem   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 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.

16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th