Multispin Clifford codes for angular momentum errors in spin systems

The physical symmetries of a system play a central role in quantum error correction. In this work we encode a qubit in a collection of systems with angular momentum symmetry (spins), extending the tools developed by Gross [J. A. Gross, Phys. Rev. Lett. 127, 010504 (2021)] for single large spins. By considering large spins present in atomic systems and focusing on their collective symmetric subspace, we develop codes with octahedral symmetry capable of correcting errors up to second order in angular momentum operators. These errors include the most physically relevant noise sources such as microwave control errors and optical pumping. We additionally explore qubit codes that exhibit distance scaling commensurate with the surface code while permitting transversal single-qubit Clifford operations.