Extensible Platforms for Bosonic Quantum Error Correction

Abstract

Bosonic quantum error correction (QEC) encodes information in the phase space of a quantum harmonic oscillator and offers a hardware-efficient path towards faulttolerant quantum information processing. With superconducting circuits, bosonic QECusing the Gottesman-Kiteav-Preskill (GKP) encoding has been achieved using the high-Q mode of a macroscopic 3D microwave cavity controlled via fixedfrequency transmon qubits [1, 2, 3, 4, 5, 6]. To date, 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 logical lifetimes that are upper-bounded by approximately ∼ 10T1. In this thesis, we replace the transmon with a heavy-fluxonium control qubit, which has been shown to possess bit-flip lifetimes in excess of 1 millisecond [7, 8, 9, 10]. Furthermore, we propose using the asymmetrically threaded SQUID as 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. Finally, with an accelerated error correction rate, we can use a lower-Q planar resonator to store logical quantum information in an extensible and fully 2D architecture.