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arXiv · 2212.14399

Quantum Mass Production Theorems

William Kretschmer
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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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William Kretschmer. 2022-12-29. Quantum Mass Production Theorems. https://doi.org/10.4230/lipics.tqc.2023.10

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