Asymptotically good bosonic Fock state codes: Exact and approximate
This addresses error correction in quantum systems like bosonic codes, but it appears incremental as it builds on existing methods for classical codes and PI codes.
The paper tackles the problem of constructing error-correcting codes for multi-mode Fock states against amplitude damping noise, showing equivalence between exact and approximate correction and building asymptotically good codes with bounded per-mode occupancy to enhance system stability.
We examine exact and approximate error correction for multi-mode Fock state codes protecting against the amplitude damping noise. Based on a new formalization of the truncated amplitude damping channel, we show the equivalence of exact and approximate error correction for Fock state codes against random photon losses. Leveraging the recently found construction method based on classical codes with large distance measured in the $\ell_1$ metric, we construct asymptotically good (exact and approximate) Fock state codes. These codes have an additional property of bounded per-mode occupancy, which increases the coherence lifetime of code states and reduces the photon loss probability, both of which have a positive impact on the stability of the system. Using the relation between Fock state code construction and permutation invariant (PI) codes, we also obtain families of asymptotically good qudit PI codes as well as codes in monolithic nuclear state spaces.