QAC0 可以制备任意对数量子比特态

中文摘要 AI 辅助

$\mathsf{QAC}^0$ 是通过将局部电路类 $\mathsf{QNC}^0$ 扩展为包含任意宽度 Toffoli 门的非局域相互作用而得到的常数深度 $\mathrm{poly}(n)$-辅助比特电路类。据信它弱于其对应类 $\mathsf{QNC}^0_f$，后者通过包含任意宽度 FANOUT 门获得（$\mathsf{QAC}^0 \subseteq \mathsf{QNC}^0_f$ [Moo99]）。在本文中，我们证明每个 $O(\log n)$-量子比特态都可以由 $\mathrm{poly}(n)$-辅助比特的 $\mathsf{QAC}^0$ 电路精确且干净地制备。此前已知的用于任意此类态的 $\mathrm{poly}(n)$-辅助比特电路仅通过额外访问 FANOUT 或 QRAM（索引）门获得 [Ros21b, GGJ26b]，这两者均未知是否属于 $\mathsf{QAC}^0$。等价地，先前在 $\mathsf{QAC}^0$ 中构造任意 $n$-量子比特态的电路需要双指数大小，而我们获得了指数因子的改进。

英文摘要

$\mathsf{QAC}^0$ is the class of constant-depth $\mathrm{poly}(n)$-ancilla circuits obtained by extending $\mathsf{QNC}^0$, the class of local circuits, to include nonlocal interactions via arbitrary width Toffoli gates. It is believed to be weaker than its counterpart, $\mathsf{QNC}^0_f$, obtained by including arbitrary-width FANOUT gates instead ($\mathsf{QAC}^0 \subseteq \mathsf{QNC}^0_f$ [Moo99]). In this note, we show that every $O(\log n)$-qubit state can be exactly and cleanly prepared by a $\mathrm{poly}(n)$-ancilla $\mathsf{QAC}^0$ circuit. Previous known $\mathrm{poly}(n)$-ancilla circuits for arbitrary such states are only known via additional access to either FANOUT or QRAM (indexing) gates [Ros21b, GGJ26b], neither of which are known to be in $\mathsf{QAC}^0$. Equivalently, prior constructions of arbitrary $n$-qubit states in $\mathsf{QAC}^0$ require doubly exponential size and we obtain an exponential factor improvement.

发表机构

• University of California at Berkeley（加州大学伯克利分校）

机构由 AI 辅助整理，请以论文原文为准。