Teleportation-based quantum error correction of multimode Gottesman-Kitaev-Preskill states

In order to achieve fault-tolerant quantum computing, we must make use of quantum error correction schemes designed to protect the physical information of the system used from decoherence [1]. A promising way to preserve such physical information is using the multimode Gottesman-Kitaev-Preskill (GKP) encoding, which encodes a single logical qubit into the infinitely large Hilbert space of multiple harmonic oscillators [2]. Typical protocols to correct multimode GKP states are based on Steane-type correction circuits, consisting of operations based on quadrature-quadrature interactions [3]. However, these interactions do not preserve the shape of the gaussian envelope describing the GKP state, distorting it and injecting more energy into the system. This leads to enhanced errors on the GKP state we wish to correct, decreasing its logical lifetime [4]. In this work, we propose a continuous-variable teleportation method for multimode GKP codes, consisting uniquely of passive gaussian transformation [5]. This technique allows us to effectively correct multimode GKP states while keeping their envelope intact and preventing the system’s energy to be increase.

[1] J. Preskill, Quantum 2, 79 (2018).

[2] D. Gottesman et al., Phys. Rev. A 64, 012310 (2001).

[3] B. Royer et al., PRX Quantum 3, 010335 (2022).

[4] K. Noh et al., PRX Quantum 3, 010315 (2022).

[5] C. Weedbrook et al., Phys. Rev. A 84, 621 (2012).