  Reducing decoherence is an essential step toward realizing general-purpose
quantum computers beyond the present noisy intermediate-scale quantum (NISQ)
computers. To this end, dynamical decoupling (DD) approaches in which external
fields are applied to qubits are often adopted. We numerically study DD using a
two-level model system (qubit) under the influence of Markovian decoherence by
using quantum optimal control theory with slightly modified settings, in which
the physical objective is to maximally create and maintain a specified
superposition state in a specified control period. An optimal pulse is
numerically designed while systematically varying the values of dephasing,
population decay, pulse fluence, and control period as well as using two kinds
of objective functionals. Although the decrease in purity due to the
decoherence gives rise to the upper limit of the target expectation value,
i.e., the saturated value, the optimally shaped pulse effectively deals with
the decoherence by gradually creating the target superposition state to realize
the saturated value as much as possible.
