We consider quantum circuits composed of single-qubit operations and global entangling gates generated by Ising-type Hamiltonians. It is shown that such circuits can implement a large class of unitary operators commonly used in quantum algorithms at a very low cost—using a constant or effectively constant number of global entangling gates. Specifically, we report constant-cost implementations of Clifford operations with and without ancillae, constant-cost implementation of the multiply-controlled gates with linearly many ancillae, and an $\mathrm{O}({\log }^{*}(n))$ cost implementation of the $n$-controlled single-target gates using logarithmically many ancillae. This shows a significant asymptotic advantage of circuits enabled by the global entangling gates.

中文翻译：

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使用全局交互的 Clifford 操作和多重控制门的恒定成本实现

我们考虑由单量子比特运算和由伊辛型哈密顿量生成的全局纠缠门组成的量子电路。结果表明，此类电路可以以非常低的成本实现量子算法中常用的一大类酉算子——使用恒定或有效恒定数量的全局纠缠门。具体来说，我们报告了带有和不带有附属项的 Clifford 操作的恒定成本实现、具有线性多个附属项的乘法控制门的恒定成本实现，以及一个$\mathrm{欧}({\mathrm{日志}}^{*}(n))$实施成本$n$-使用对数多的附属物控制单目标门。这显示了由全局纠缠门启用的电路的显着渐近优势。