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Quantum Mass Production Theorems (2212.14399v2)
Published 29 Dec 2022 in quant-ph, cs.CC, and cs.DS
Abstract: 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 $O(4n)$ 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.