Decoding Multimode Gottesman-Kitaev-Preskill Codes with Noisy Auxiliaries

In order to achieve fault-tolerant quantum computing, we make use of quantum error correction schemes designed to protect the logical information of the system from decoherence. A promising way to preserve such 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. Usual protocols to correct multimode GKP states are based on Steane-type quantum error correction circuits. These steane-type circuits consist of auxiliary state preparation, two-mode squeezing operations, measurements and decoding. In this work, we focus on improving the latter. More precisely, we propose a decoder that considers the noise present on the auxiliary states. We do so by tracking the correlations between errors on different modes spreading throughout the circuit. Overall, for each different multimode GKP code studied, the probability of error can be decreased by at least an order of magnitude, yielding more robust quantum computation.