  We prove that for any $n$-qubit unitary transformation $U$ and for any $r =
2^{o(n / \log n)}$, there exists a quantum circuit to implement $U^{\otimes r}$
with at most $O(4^n)$ gates. This asymptotically equals the number of gates
needed to implement just a single copy of a worst-case $U$. We also establish
analogous results for quantum states and diagonal unitary transformations. Our
techniques are based on the work of Uhlig [Math. Notes 1974], who proved a
similar mass production theorem for Boolean functions.
