  We prove a query complexity variant of the weak polynomial Freiman-Ruzsa
conjecture in the following form. For any $\epsilon > 0$, a set $A \subset
\mathbb{Z}^d$ with doubling $K$ has a subset of size at least
$K^{-\frac{4}{\epsilon}}|A|$ with coordinate query complexity at most $\epsilon
\log_2 |A|$.
  We apply this structural result to give a simple proof of the "few products,
many sums" phenomenon for integer sets. The resulting bounds are explicit and
improve on the seminal result of Bourgain and Chang.
