Quantum control and noise protection of a Floquet 0−π qubit

Time-periodic systems allow engineering new effective Hamiltonians from limited physical interactions. For example, the inverted position of the Kapitza pendulum emerges as a stable equilibrium with rapid drive of its pivot point. In this work we propose the Kapitzonium: a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum. Under periodic driving, the bit- and phase-flip rates of the emerging qubit states are exponentially suppressed with respect to the ratio of the effective Josephson energy to charging energy. However, we find that dissipation causes leakage out of the Floquet qubit subspace. We engineer a passive cooling scheme to stabilize the qubit subspace, which is crucial for high-fidelity quantum control under dissipation. Furthermore, we introduce a hardware-efficient fluorescence-based method for qubit measurement and discuss the experimental implementation of the Floquet qubit. Our work provides the fundamental steps to develop more complex Floquet quantum systems from the ground up to realize large-scale protected engineered dynamics.