Abstract
A connected Lie group G is generated by its two 1-parametric subgroups exp(tX), exp(tY) if and only if the Lie algebra of G is generated by {X, Y}. We consider decompositions of elements of G into a product of such exponentials with times t > 0 and study the problem of minimizing the total time of the decompositions for a fixed element of G. We solve this problem for the group SU 2 and describe the structure of the time-optimal decompositions.
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Billig, Y. Time-optimal decompositions in SU(2). Quantum Inf Process 12, 955–971 (2013). https://doi.org/10.1007/s11128-012-0447-y
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DOI: https://doi.org/10.1007/s11128-012-0447-y