Encoding qubits in multiple oscillators

Codes based on harmonic oscillators are a promising approach to quantum error correction. Due to their long lifetimes and their large intrinsic Hilbert space, harmonic oscillators such as microwave cavities provide a hardware-efficient approach to error correction compared to qubit register-based codes. In particular, the grid codes introduced by Gottesman, Kitaev and Preskill (GKP) have been numerically and experimentally shown to exhibit long logical lifetimes. However, a recurring challenge with bosonic codes is that they are limited by the lifetime of the ancilla used for quantum control of bosonic modes.

In this talk, I will show that we can tackle this challenge by encoding a logical qubit in multiple modes instead of a single one. Interestingly, these multimode codes have several properties that make them an attractive option as the basis for a quantum computer. More precisely, we introduce a method to autonomously stabilize the code space of multimode GKP codes, and introduce a two-mode grid code which has improved properties with respect to traditional single mode GKP codes. When stabilized with a qubit ancilla, we numerically show that this code has improved robustness against ancilla decay.