Erdős Problem #485 — Terms in the square of a sparse polynomial

For $k\geq1$, let $Q_k$ be the least possible number of nonzero coefficients of $P(x)^2$, where $P\in\mathbb{Q}[x]$ has exactly $k$ nonzero coefficients. Must $Q_k\to\infty$ as $k\to\infty$?