Autonomous quantum error correction of Gottesman-Kitaev-Preskill states, Part 2: Theory

Bosonic codes aim to take advantage of the large Hilbert space offered by harmonic oscillators to encode logical qubits with some degrees of redundancy within a single physical system, thus providing a possible route for hardware-efficient fault-tolerant quantum computing. Most notably, Gottesman-Kitaev-Preskill (GKP) states are shown to be resilient to the main source of error in most bosonic systems, that is, photon loss. In part 1, we present experimental results in superconducting circuits demonstrating fully autonomous stabilization of GKP states, which led to quantum error correction close to the break-even threshold without any postselection. In this presentation (part 2), we present the theoretical background and numerical simulations that guided those experiments, and discuss fundamental insights into the stabilization protocol.