  We provide a technique to obtain provably optimal control sequences for
quantum systems under the influence of time-correlated multiplicative control
noise. Utilizing the circuit-level noise model introduced in [Phys. Rev.
Research 3, 033229(2021)], we show that we can map the problem of finding such
a sequence to a convex optimization problem with guaranteed optimality that
follows from the convexity. We also show that this technique is compatible with
more general off-axis time-correlated dephasing noise. In spite of losing
provable optimality, numerically optimized control sequences under this
scenario can still achieve nearly optimal performance when the control noise is
strong relative to the dephasing contribution. This approach will enable the
development of optimal quantum logic gates in systems where noise due to
amplitude drifts in the control is strong relative to dephasing such as in
ion-trap based quantum computers or in the limit of fast control.
