Encoding Qubits in Multimode Grid States
Baptiste Royer, Shraddha Singh, S. M. Girvin · PRX Quantum · 2022
Encoding logical quantum information in harmonic oscillator modes is a promising and hardwareefficient approach to the realization of a quantum computer.In this work, we propose to encode logical qubits in grid states of an ensemble of harmonic oscillator modes.We first discuss general results about these multimode bosonic codes; how to design them, how to practically implement them in different experimental platforms, and how lattice symmetries can be leveraged to perform logical non-Clifford operations.We then introduce in detail two two-mode grid codes based on the hypercubic and D 4 lattices, respectively, showing how to perform a universal set of logical operations.We demonstrate numerically that multimode grid codes have, compared to their single-mode counterpart, increased robustness against propagation of errors from ancillas used for error correction.Finally, we highlight some interesting links between multidimensional lattices and single-mode grid codes concatenated with qubit codes.