Fast naviation with icosahedral golden gates

IF 0.7 4区 物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS Quantum Information & Computation Pub Date : 2023-09-01 DOI:10.26421/qic23.11-12-1
Terrence R Blackman, Zachary Stier
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Abstract

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.
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快速导航与二十面体金门
Ross和Selinger将PU(2)的对角线元素分解到距离$\varepsilon$内的算法被Parzanchevski和Sarnak采用为PU(2)的任何元素的有效概率算法,该算法使用与数字域和素数$p$相关的某些精心选择的集合中的最有效$3\log_p\frac{1}{\varepsilon^{3}}$因子。二十面体超级金门就是与$\mathbb{Q}(\sqrt{5})$相关的一组。我们利用Carvalho Pinto, Petit和Stier最近的工作将这个界限降低到$\frac{7}{3}\log_{59}\frac{1}{\varepsilon^3}$,并在Python中实现该算法。这表示与Clifford+ $T$门的类似结果相比,有了$\log_259\approx5.9$倍的改进。这是有趣的,因为二十面体门是所有超级金门中分解长度最短的。
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来源期刊
Quantum Information & Computation
Quantum Information & Computation 物理-计算机:理论方法
CiteScore
1.70
自引率
0.00%
发文量
42
审稿时长
3.3 months
期刊介绍: Quantum Information & Computation provides a forum for distribution of information in all areas of quantum information processing. Original articles, survey articles, reviews, tutorials, perspectives, and correspondences are all welcome. Computer science, physics and mathematics are covered. Both theory and experiments are included. Illustrative subjects include quantum algorithms, quantum information theory, quantum complexity theory, quantum cryptology, quantum communication and measurements, proposals and experiments on the implementation of quantum computation, communications, and entanglement in all areas of science including ion traps, cavity QED, photons, nuclear magnetic resonance, and solid-state proposals.
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