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We consider protecting a Hadamard operation from independent dephasing, bitflipping, and dissipation. These environment-induced errors are represented bythree uncorrelated reservoirs of thermalized bosons and we show that theprotection is achievable through continuous dynamical decoupling. We find that,to decouple the Hadamard evolution from the environmental influence, we need acontrol field of higher frequency if the boson spectral density is super-ohmicthan if it is ohmic. We also study the relevance of bit flipping anddissipation to the gate fidelity when it is protected from dephasing, showinghow robust this partial protection is against these other perturbations.Finally, we calculate an efficient field arrangement capable of protectingsimultaneously the gate operation from these three error classes.

Continuously decoupling a Hadamard quantum gate from independent classes of errors