  Nowadays most of superconducting quantum processors use charge qubits of a
transmon type. They require implementation of energy efficient qubit state
control scheme. A promising approach is the use of superconducting digital
circuits operating with single-flux-quantum (SFQ) pulses. The duration of SFQ
pulse control sequence is typically larger than that of conventional microwave
drive pulses but its length can be optimized for the system with known
parameters. Here we introduce a genetic algorithm for unipolar or bipolar SFQ
control sequence search that minimize qubit state leakage from the
computational subspace. The algorithm is also able to find a solution in the
form of a repeating subsequence in order to save memory on the control chip.
Its parallel implementation can find the appropriate sequence for arbitrary
system parameters from a practical range in a reasonable time. The algorithm is
illustrated by the example of the rotation gate around the axis by an angle
$\pi/2$ with fidelity over 99.99%. In this paper, we present the results for a
single-qubit system, but in the future we will apply the developed approach to
study a system of two qubits.
