On-chip bosonic quantum error correction with a parametrically coupled heavy fluxonium control qubit

Bosonic quantum error correction (QEC) encodes information in the phase space of a quantum harmonic oscillator and offers a hardware-efficient path towards fault-tolerant quantum information processing. With superconducting circuits, bosonic QEC using the Gottesman-Kiteav-Preskill (GKP) code has been achieved within the high-Q mode of a macroscopic 3D microwave cavity dispersively coupled to a fixed-frequency transmon qubit. However, all previous demonstrations have been limited by bit-flips in the transmon control qubit (with typical T₁ lifetimes on the order of 100 microseconds), resulting in GKP logical lifetimes that are upper-bounded by approximately ~10T₁. In this work, we instead use a heavy fluxonium as a control qubit, with bit-flip lifetimes in excess of 1 millisecond. Furthermore, we propose using a microwave-activated three-wave mixing coupler to yield faster GKP error-correction rates while suppressing inherited nonlinearity in our bosonic mode. As compared to direct dispersive coupling, this parametric coupling enables us to use a heavier, and therefore more bit-flip-protected, fluxonium qubit. With an accelerated error-correction rate, we can use a planar resonator to store logical quantum information in an extensible and fully 2D architecture. Finally, we report on experimental progress towards the creation and manipulation of Gottesman-Kitaev-Preskill states using this system.