Permutation-invariant Holstein-Primakoff spin codes for local and collective noise
Phys. Rev. A 114, 022467 – Published 27 August, 2026
DOI: https://doi.org/10.1103/vrxx-bqlg
Abstract
Quantum error correction is essential for fault-tolerant quantum computation, yet most existing codes rely on local control and stabilizer measurements that are difficult to implement in systems dominated by collective interactions. Inspired by S. Omanakuttan and T. J. Volkoff, Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles, Phys. Rev. A 108, 022428 (2023), we develop a general framework for Holstein-Primakoff (HP) spin codes that maps continuous-variable bosonic codes onto permutation-invariant spin ensembles via the Holstein-Primakoff approximation. We show that HP codes are robust to both collective and local spin noise and propose an explicit measurement-free local error recovery procedure to convert local noise into correctable collective spin errors.
