Protecting superconducting qubits from low-frequency noise by operating them on dynamical sweet-spot manifolds has proven to be a promising setup, theoretically as well as experimentally. These dynamical sweet spots are induced by an externally applied Floquet drive, and various drive forms have been studied in different types of qubits. In this work we study the effects of using two-tone drives on the applied magnetic flux of the form ${\varphi }_{\mathrm{ac}}\left(t\right)={\varphi }_{m}cos\left(m{\omega }_{\mathrm{d}}t\right)+{\varphi }_{n}cos(n{\omega }_{\mathrm{d}}t+\phi )$, where $m,n\in {\mathbb{N}}_{>0}$, on the coherence times of fluxonium qubits. Through analysis using perturbation theory in the strong-drive limit, we show which sets of drive parameters increase the dephasing times, based upon first-order coupling between Floquet modes. These are further analyzed using numerical calculations. We further show that this type of drive allows for more tunability of the quasienergy spectrum, creating higher and wider peaks of the dephasing time without affecting the relaxation times too strongly. Lastly, we show that temporarily modulating the drive form using a second commensurable tone can be used to implement an improved phase gate compared to implementations with a single tone, supported by Monte Carlo simulations.

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• Quantum engineering
• Quantum gates
• Superconducting qubits
• Monte Carlo methods
• Numerical techniques