SHORT PATHS IN PU(2)

Parzanchevski-Sarnak [1] recently adapted an algorithm of Ross-Selinger [2] for factorization of PU(2)-diagonal elements to within distance epsilon into an efficient probabilistic algorithm for any PU(2)-element, using at most 3 log(p)(1/epsilon(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 [3] to improve this to 7/3log(2) (1/epsilon(3)), and implement the algorithm in Haskell.

Automated summary

The algorithm developed by Parzanchevski-Sarnak adapts Ross-Selinger's method to efficiently factorize PU(2)-diagonal elements within a distance epsilon, extending it to any PU(2)-element. By leveraging Carvalho Pinto-Petit's recent work, the algorithm has been further improved and implemented in Haskell, with the use of certain well-chosen sets of factors.