论文标题
量子质量生产定理
Quantum Mass Production Theorems
论文作者
论文摘要
我们证明，对于任何$ n $ qubit的统一转换$ u $，对于任何$ r = 2^{o（n / \ log n）} $，存在一个量子电路来实现$ u^{\ otimes r} $，最多$ o（4^n）$ GATES。该渐近地等于仅实现最坏情况$ u $的单个副本所需的门数。我们还为量子状态和对角线统一转换建立了类似的结果。我们的技术基于Uhlig的工作[Math。注释1974]，他证明了布尔功能的类似质量生产定理。
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.
