  Given $v_1,\ldots, v_m\in\mathbb{C}^d$ with $\|v_i\|^2= \alpha$ for all
$i\in[m]$ as input and suppose $\sum_{i=1}^m | \langle u, v_i \rangle |^2 = 1$
for every unit vector $u\in\mathbb{C}^d$, Weaver's discrepancy problem asks for
a partition $S_1, S_2$ of $[m]$, such that $\sum_{i\in S_{j}} |\langle u, v_i
\rangle|^2 \leq 1 -\theta$ for some universal constant $\theta$, every unit
vector $u\in\mathbb{C}^d$ and every $j\in\{1,2\}$. We prove that this problem
can be solved deterministically in polynomial time when $m\geq 49 d^2$.
