can any subgroup of the unitary group of full matrix alg $M_d(\mathbb{C})$ be approximated on finite
sets by a finite subgroup?

i.e. is the following True or false?
Let $n, d$ be positive integers and let
$u_1,..., u_n$ be in the unitary group $U_d=U (M_d(\mathbb{C}))$ of $M_d(\mathbb{C})$. Then for
every $\epsilon > 0$ there are $v_1, ..., v_n$ in $U_d$ such that
$\| u_k - v_k \| < \epsilon$ for $k = 1, .., n$ and such that the
subgroup of $U_d$ that $v_1, ..., v_n$ generate is finite.


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