Bosonic error correction using a bit-flip-protected control qubit: Part 1

Bosonic quantum error correction (QEC) involves encoding information in the phase space of a quantum harmonic oscillator, and offers a hardware-efficient path towards fault-tolerant quantum information processing. In superconducting circuits, bosonic QEC has been achieved using 3D cavity resonators controlled via fixed-frequency transmon qubits [1-4]. 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 logical lifetimes that are upper-bounded by approximately ~10T1. In this work, we propose replacing the transmon with a heavy-fluxonium qubit, which has been shown to possess T1 lifetimes in excess of 1 millisecond [5-7]. By embedding the fluxonium qubit within a 3D cavity architecture, we demonstrate bit-flip-protected bosonic QEC using the Gottesman-Kiteav-Preskill (GKP) encoding.

In this part of a multi-part talk, we discuss the theoretical background and experimental design considerations for this project.

[1] N. Ofek et al., Nature 536, 441–445 (2016).

[2] J. Gertler et al., Nature 590, 243–248 (2021).

[3] L. Hu et al., Nat. Phys. 15, 503–508 (2019).

[4] P. Campagne-Ibarcq et al., Nature 368–372 (2020).

[5] N. Earnest et al., Phys. Rev. Lett. 120, 150504 (2018).

[6] Y. Lin et al., Phys. Rev. Lett. 120, 150503 (2018).

[7] H. Zhang et al., Phys. Rev. X 11, 011010 (2021).