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arXiv · 2012.04695

Short paths in PU(2)

Zachary Stier
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Abstract

Parzanchevski and Sarnak recently adapted an algorithm of Ross and Selinger for factorization of PU(2)-diagonal elements to within distance $\varepsilon$ into an efficient probabilistic algorithm for any PU(2)-element, using at most $3\log_p\frac{1}{\varepsilon^3}$ factors from certain well-chosen sets. The Clifford+$T$ gates are one such set arising from $p=2$. In that setting, we leverage recent work of Carvalho Pinto and Petit to improve this to $\frac{7}{3}\log_2\frac{1}{\varepsilon^3}$, and implement the algorithm in Haskell.

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Zachary Stier. 2020-12-08. Short paths in PU(2). https://arxiv.org/abs/2012.04695

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