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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Keywords Controllability of vector fields, Quantum control, Time-optimal decompositions
Persistent URL dx.doi.org/10.1007/s11128-012-0447-y
Journal Quantum Information Processing
Billig, Y. (2013). Time-optimal decompositions in SU(2). Quantum Information Processing, 12(2), 955–971. doi:10.1007/s11128-012-0447-y