Optimal two-mode bosonic loss codes from finite group symmetry
Abstract
Photon loss is a dominant noise process in bosonic quantum hardware, including superconducting cavities. Fixed-total-photon-number qubit encodings in two bosonic modes retain the loss-detection advantage of dual-rail qubits while supporting photon loss correction. Optimizing entanglement fidelity in this setting for 4≤ n≤25 over arbitrary encoders and decoders reveals finite-group structure in every best-found code: 11 correspond to two-dimensional irreducible representations and 11 to reducible ones. Motivated by this emergence, we derive the necessary-and-sufficient Knill-Laflamme conditions for arbitrary finite-group-invariant codes, reducing their construction to equations on representation multiplicity spaces. For every finite subgroup of SU(2) and every tensor rank, we explicitly construct the minimum number of operators required to impose all corresponding loss-correction constraints. These results produce analytic counterparts to most numerical codes and predict constructions missed by the initial search. Exact MacWilliams-Farkas certificates show that our codes achieve the maximum possible loss distance in 21 of the 22 sectors, and we prove that the resulting distance bound is monotone in total photon number. Beyond the scan, we identify a binary-polyhedral sequence with photon number nd=⌈(3d2+1)/4⌉ and construct each corresponding code through distance d=10. To our knowledge, the constructed (n,d)=(28,6),(49,8),(76,10) codes give the smallest reported n for their respective distances; all members through d=9 attain the fixed-n LP distance bound. Together, these constructions, certificates, and a symmetry-reduced constraint count provide evidence for an infinite code family conjectured to attain every distance at the minimum photon number.
Related
- Bosonic codes from compact phase spaces
- Symmetry-resolved parent Hamiltonians for entangled bosonic cat resources
- Asymptotically good bosonic Fock state codes
- Bosonic Loss Codes with Bounded Occupation
- Exact SU(N) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states
BibTeX
@misc{manes2026optimal,
title = {{Optimal two-mode bosonic loss codes from finite group symmetry}},
author = {Argyris Giannisis Manes and Mahadevan Subramanian and Liang Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00561},
eprint = {2610.00561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00561},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal two-mode bosonic loss codes from finite group symmetry
AU - Argyris Giannisis Manes
AU - Mahadevan Subramanian
AU - Liang Jiang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00561
UR - https://arxiv.org/abs/2610.00561
AB - Photon loss is a dominant noise process in bosonic quantum hardware, including superconducting cavities. Fixed-total-photon-number qubit encodings in two bosonic modes retain the loss-detection advantage of dual-rail qubits while supporting photon loss correction. Optimizing entanglement fidelity in this setting for 4≤ n≤25 over arbitrary encoders and decoders reveals finite-group structure in every best-found code: 11 correspond to two-dimensional irreducible representations and 11 to reducible ones. Motivated by this emergence, we derive the necessary-and-sufficient Knill-Laflamme conditions for arbitrary finite-group-invariant codes, reducing their construction to equations on representation multiplicity spaces. For every finite subgroup of SU(2) and every tensor rank, we explicitly construct the minimum number of operators required to impose all corresponding loss-correction constraints. These results produce analytic counterparts to most numerical codes and predict constructions missed by the initial search. Exact MacWilliams-Farkas certificates show that our codes achieve the maximum possible loss distance in 21 of the 22 sectors, and we prove that the resulting distance bound is monotone in total photon number. Beyond the scan, we identify a binary-polyhedral sequence with photon number n_d=⌈(3d^2+1)/4⌉ and construct each corresponding code through distance d=10. To our knowledge, the constructed (n,d)=(28,6),(49,8),(76,10) codes give the smallest reported n for their respective distances; all members through d=9 attain the fixed-n LP distance bound. Together, these constructions, certificates, and a symmetry-reduced constraint count provide evidence for an infinite code family conjectured to attain every distance at the minimum photon number.
ER -