Short paths in PU(2)
Parzanchevski--Sarnak \cite{PS} recently adapted an algorithm of Ross--Selinger \cite{RS16} for factorization of $\PU(2)$-diagonal elements to within distance $\eps$ into an efficient probabilistic algorithm for any $\PU(2)$-element, using at most $3\log_p(\nicefrac{1}{\eps^3})$ 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--Petit \cite{CPP} to improve this to $\frac{7}{3}\log_2(\nicefrac{1}{\eps^3})$, and implement the algorithm in Haskell.
Keyword(s):
1991 ◽
Vol 49
◽
pp. 38-39
Keyword(s):
Keyword(s):
1921 ◽
Vol 3
(6supp)
◽
pp. 561-562
Keyword(s):
1986 ◽
Vol 13
(1)
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pp. 78-85
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