论文标题
快速导航与二十面体金门
Fast Navigation with Icosahedral Golden Gates
论文作者
论文摘要
Ross and Selinger的算法将PU（2）的对角线元素分解为距离内$ \ Varepsilon $，由Parzanchevski和Sarnak改编为有效的概率算法，用于使用PU（2）的任何一个最有效的$ 3 \ log_p \ frac \ frac} $ pu（2）的任何元素。与数字字段和Prime $ p $相关的精心选择的集合。 Icosahedral超级金门是与$ \ Mathbb {q}（\ sqrt {5}）$相关的这样的集合。我们利用Carvalho Pinto，Petit和Stier的最新工作将其减少到$ \ frac {7} {3} {3} \ log_ {59} \ frac {1} {\ varepsilon^3} $，我们在Python中实现了Algorithm。这代表了与Clifford+$ t $门的类似结果相比，$ \ log_259 \ oft.5.9 $的乘法因子的改进。这很有趣，因为在所有超级金门大门中，二十面体大门的分解长度最短。
An algorithm of Ross and Selinger for the factorization of diagonal elements of PU(2) to within distance $\varepsilon$ was adapted by Parzanchevski and Sarnak into an efficient probabilistic algorithm for any element of PU(2) using at most effective $3\log_p\frac{1}{\varepsilon^{3}}$ factors from certain well-chosen sets associated to a number field and a prime $p$. The icosahedral super golden gates are one such set associated to $\mathbb{Q}(\sqrt{5})$. We leverage recent work of Carvalho Pinto, Petit, and Stier to reduce this bound to $\frac{7}{3}\log_{59}\frac{1}{\varepsilon^3}$, and we implement the algorithm in Python. This represents an improvement by a multiplicative factor of $\log_259\approx5.9$ over the analogous result for the Clifford+$T$ gates. This is of interest because the icosahedral gates have shortest factorization lengths among all super golden gates.
