Quantum Error Correction with the Toric-GKP Code

Understand

We examine the performance of the single-mode GKP code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors.

• We show how one can optimize the tracking of errors in repeated noisy error correction for the GKP code.
• We do this by examining the maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean path-integral modeling a particle in a random cosine potential.
• We demonstrate the efficiency of a minimum-energy decoding strategy as a proxy for the path integral evaluation.