  Efficient implementation of quantum algorithms requires single- or
multi-qubit gates with high fidelity. In this report, we report that the
fidelity of single-qubit gate operations on open quantum systems has a maximum
value corresponding to an optimum value of the drive-amplitude in the presence
of drive-induced decoherence. To show this, we use a previously reported
fluctuation-regulated quantum master equation [Phys. Rev. A 97, 063837 (2018)].
The fidelity is found to be a function of the drive-induced dissipative terms
as well as the relaxation terms arising from the qubit-environment coupling; as
a result, it behaves non-monotonically with the drive-amplitude. The existence
of an optimum drive-amplitude implies that the single-qubit operations on open
quantum systems would have an optimal clock speed.
