I can't be the first one to think of this and there must be a reason nobody design cryptosystem off this problem.
Let's define MECC as matrix of elliptic curve points, and MI as matrix of non-negative integers.
Given a MECC $G$, MI $v$, and MECC $P=v\cdot G$. How would a quantum computer calculate $v$ from $P$ and $G$?