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Peer-reviewedCC BY 4.0Quantum

Asymptotically good bosonic Fock state codes

  • Dor Elimelech1,2
  • Arda Aydin2
  • Alexander Barg2,1,3
  1. 1Joint Center for Quantum Information and Computer Science (QuICS), UMD/NIST
  2. 2Institute for Systems Research, University of Maryland, College Park, MD 20742
  3. 3Department of ECE, University of Maryland, College Park, MD 20742
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Abstract

We study the error-correction properties of multi-mode Fock-state codes under amplitude-damping (AD) noise, focusing on the asymptotic regime in which the total excitation of the code states grows without limit and the number of photon losses induced by the noise scales linearly with it. In this setting, existing code families, which correct only sublinearly many photon losses, do not protect against amplitude-damping (AD) noise with a constant loss parameter. As our main result, we address this gap by constructing asymptotically good Fock-state codes relying on random classical codes in the discrete simplex. Unlike many standard constructions of random quantum codes, our construction introduces randomness through the underlying classical indexing structure. Randomization also enables another desirable feature: bounded per-mode occupancy, which limits the number of photons in any individual mode and thereby increases the coherence lifetime of the code states. Finally, via a relation between Fock-state codes and permutation-invariant codes, our results also yield asymptotically good families of qudit permutation-invariant codes as well as codes in monolithic nuclear state spaces.

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Cite

BibTeXRIS
BibTeX
@article{elimelech2026asymptotically,
  title = {{Asymptotically good bosonic Fock state codes}},
  author = {Dor Elimelech and Arda Aydin and Alexander Barg},
  journal = {Quantum},
  year = {2026},
  month = oct,
  doi = {10.22331/q-2026-10-20-2240},
  url = {https://quantum-journal.org/papers/q-2026-10-20-2240/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Asymptotically good bosonic Fock state codes
AU  - Dor Elimelech
AU  - Arda Aydin
AU  - Alexander Barg
PY  - 2026
DA  - 2026/10/20
JO  - Quantum
DO  - 10.22331/q-2026-10-20-2240
UR  - https://quantum-journal.org/papers/q-2026-10-20-2240/
AB  - We study the error-correction properties of multi-mode Fock-state codes under amplitude-damping (AD) noise, focusing on the asymptotic regime in which the total excitation of the code states grows without limit and the number of photon losses induced by the noise scales linearly with it. In this setting, existing code families, which correct only sublinearly many photon losses, do not protect against amplitude-damping (AD) noise with a constant loss parameter. As our main result, we address this gap by constructing asymptotically good Fock-state codes relying on random classical codes in the discrete simplex. Unlike many standard constructions of random quantum codes, our construction introduces randomness through the underlying classical indexing structure. Randomization also enables another desirable feature: bounded per-mode occupancy, which limits the number of photons in any individual mode and thereby increases the coherence lifetime of the code states. Finally, via a relation between Fock-state codes and permutation-invariant codes, our results also yield asymptotically good families of qudit permutation-invariant codes as well as codes in monolithic nuclear state spaces.
SN  - 2521-327X
ER  -