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We study reliable quantum information processing (QIP) under two differenttypes of environment. First type is Markovian exponential decay, and theappropriate elementary strategy of protection of qubit is to apply fast gates.The second one is strongly non-Markovian and occurs solely during operations onthe qubit. The best strategy is then to work with slow gates. If the two typesare both present, one has to optimize the speed of gate. We show that such atrade-off is present for a single-qubit operation in a semiconductor quantumdot implementation of QIP, where recombination of exciton (qubit) is Markovian,while phonon dressing gives rise to the non-Markovian contribution.Comment: 4 pages, 1 figure; final versio

Optimal strategy for a single-qubit gate and the trade-off between opposite types of decoherence