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We consider the leakage suppression problem of a three-level system in whichthe first two levels are the qubit system and the third, weakly-coupled to thesecond, is the leakage state. We show that phase- and amplitude-controlled two(three) pulses are sufficient for arbitrary qubit controls from the ground (anarbitrary) initial state, with leakage suppressed up to the first order ofperturbation without additional pulse-area cost. A proof-of-principleexperiment was performed with shaped femtosecond optical pulses and atomicrubidium showing a good agreement with the theory.

Leakage suppression by ultrafast pulse shaping