Quantum Mass Production Theorems

• URL: http://arxiv.org/abs/2212.14399v2
• Date: Tue, 2 May 2023 18:41:54 GMT
• Title: Quantum Mass Production Theorems
• Authors: William Kretschmer
• Abstract summary: We prove that for any $n$-qubit unitary transformation $U$ there exists a quantum circuit to implement $Uotimes r$ with at most $O(4n)$ gates. We also establish results for quantum states and diagonal unitary transformations.
• Score: 0.22843885788439797
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $O(4^n)$ 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.

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