Encoding qubits in multimode grid states

TL;DR

This paper proposes encoding logical qubits in multimode grid states of harmonic oscillators, demonstrating their design, implementation, and enhanced error robustness over single-mode codes, with potential for universal quantum computation.

Contribution

It introduces multimode grid codes based on specific lattices, detailing their design, implementation, and advantages over single-mode codes, including increased error resilience.

Findings

Numerical evidence shows increased robustness against error propagation.

Detailed methods for implementing two-mode grid codes in different platforms.

Connections between multidimensional lattices and concatenated single-mode codes.

Abstract

Encoding logical quantum information in harmonic oscillator modes is a promising and hardware-efficient 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 D4 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.