Protomon: A Multimode Qubit in the Fluxonium Molecule

Qubits that are intrinsically insensitive to depolarization and dephasing errors promise to significantly reduce the overhead of fault-tolerant quantum computing. At their optimal operating points, the logical states of these qubits exhibit both exponentially suppressed matrix elements and sweet spots in energy dispersion, rendering the qubits immune to depolarization and dephasing, respectively. We introduce a multimode qubit, the protomon, encoded in a fluxonium molecule circuit. Compared to the closely related $0$-$\pi$ qubit, the protomon offers several advantages in theory: resilience to circuit parameter disorder, minimal dephasing from intrinsic harmonic modes, and no dependence on static offset charge. As a proof of concept, we realize four protomon qubits. By tuning the qubits to various operating points identified with calibrated two-tone spectroscopy, we measure depolarization times ranging from 64 to 73 $\mu$s and dephasing times between 0.2 to 0.5 $\mu$s for one selected qubit. The discrepancy between the relatively short measured coherence times and theoretical predictions is not fully understood. This calls for future studies investigating the limiting noise factors, informing the direction for improving coherence times of the protomon qubit.