  Based on the recent breakthrough of Huang (2019), we show that for any total
Boolean function $f$,
  $\bullet \quad \mathrm{deg}(f) = O(\widetilde{\mathrm{deg}}(f)^2)$: The
degree of $f$ is at most quadratic in the approximate degree of $f$. This is
optimal as witnessed by the OR function.
  $\bullet \quad \mathrm{D}(f) = O(\mathrm{Q}(f)^4)$: The deterministic query
complexity of $f$ is at most quartic in the quantum query complexity of $f$.
This matches the known separation (up to log factors) due to Ambainis, Balodis,
Belovs, Lee, Santha, and Smotrovs (2017).
  We apply these results 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 $\mathrm{Q}(f)=\Omega(n)$, which is also optimal. We also show
that the approximate degree of any read-once formula on $n$ variables is
$\Theta(\sqrt{n})$.
