Autonomous quantum error correction of Gottesman-Kitaev-Preskill states, Part 1: Experiments

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 promising 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, single photon loss. Initialization and quantum error correction of GKP states have been recently demonstrated in both superconducting circuits and trapped ions. Here we present experimental results in superconducting circuits showing the stabilization of GKP states based on a recently proposed reservoir-engineering approach. In addition to cavity-ancillary qubit entangling gates and single ancillary qubit rotations, the technique uses a feedback-free reset of the ancillary qubit, making the quantum error correction protocol completely autonomous. The logical lifetime with quantum error correction is shown to be on par with the lifetime under free evolution, demonstrating autonomous quantum error correction close to the break-even threshold without any postselection.