  Precise and efficient control of quantum systems is essential to perform
quantum information processing tasks. In terms of adiabatic speedup via leakage
elimination operator approach, for a closed system, the ideal pulse control
conditions have been theoretically derived by P-Q partitioning technique.
However, it is a challenge to design the corresponding control pulses for an
open system, which requires to tackle noisy environments. In this paper, we
apply the stochastic search procedures to an open qutrit system and
successfully obtain the optimal control pulses for significant adiabatic
speedup. The calculation results show that these optimal pulses allow us to
acquire higher fidelities than the ideal pulses. The improvement of fidelity is
large for relatively strong system-bath coupling strength and high bath
temperature. For certain coupling strength and bath temperature, the maximal
improvement can be achieved for a critical characteristic frequency which
represents the memory time of the environment. Our investigation indicates that
the stochastic search procedures are powerful tools to design control pulses
for combating the detrimental effects of the environment.
