Decoding Multimode Gottesman-Kitaev-Preskill Codes with Noisy Auxiliaries

          @misc{ scivideos_PIRSA:25100150,
            doi = {10.48660/25100150},
            url = {https://pirsa.org/25100150},
            author = {Roy, Marc-Antoine},
            keywords = {},
            language = {en},
            title = {Decoding Multimode Gottesman-Kitaev-Preskill Codes with Noisy Auxiliaries},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100150 see, \url{https://scivideos.org/pirsa/25100150}}
          }
          

Abstract

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 harmonic oscillators. This type of encoding adds redundancy in the physical system by leveraging the infinitely large Hilbert space of multiple oscillators. Such redundancy can be used to increase the distance between the logical code words, protecting the logical qubit against larger errors. Usual protocols to correct multimode GKP states are based on Steane-type quantum error correction circuits. Steane-type circuits consist of auxiliary state preparation, two-mode squeezing operations, measurements and decoding. In this work, we focus on the decoding part of these protocols. More precisely, we propose a decoder that considers the noise present on the auxiliary states. Specifically, we do so by tracking the correlations between errors on different modes spreading throughout the circuit which represents the Steane-type protocol. We show that leveraging the correlations between the measurement result and the actual error affecting the multimode GKP state enables less decoding errors. Overall, for each different multimode GKP code studied, we can increase the lifetime by at least an order of magnitude, yielding more robust quantum computation.