  High-precision manipulation of multi-qubit quantum systems requires strictly
clocked and synchronized multi-channel control signals. However, practical
Arbitrary Waveform Generators (AWGs) always suffer from random signal jitters
and channel latencies that induces non-ignorable state or gate operation
errors. In this paper, we analyze the average gate error caused by clock
noises, from which an estimation formula is derived for quantifying the control
robustness against clock noises. This measure is then employed for finding
robust controls via a homotopic optimization algorithm. We also introduce our
recently proposed stochastic optimization algorithm, b-GRAPE, for training
robust controls via randomly generated clock noise samples. Numerical
simulations on a two-qubit example demonstrate that both algorithms can greatly
improve the control robustness against clock noises. The homotopic algorithm
converges much faster than the b-GRAPE algorithm, but the latter can achieve
more robust controls against clock noises.
