Sparse subsystem code[1]
Description
A geometrically local qubit, modular-qudit, or Galois-qudit subsystem stabilizer code for which the number of sites participating in each gauge-group generator and the number of gauge-group generators that each site participates in are both bounded by a constant as \(n\to\infty\).
Rate
There exists a family of sparse subsystem codes with \(d = n^{1-\epsilon}\), where \(\epsilon = O(1/\sqrt{\log n})\) [1].
Parent
Children
- Lattice subsystem code — Lattice subsystem codes are sparse subsystem codes on Euclidean geometries.
- Subsystem spacetime circuit code
Cousin
- Quantum low-density parity-check (QLDPC) code — Sparse subsystem codes reduce to QLDPC codes when there are no gauge qudits.
References
- [1]
- D. Bacon et al., “Sparse Quantum Codes From Quantum Circuits”, IEEE Transactions on Information Theory 63, 2464 (2017) arXiv:1411.3334 DOI
Page edit log
- Victor V. Albert (2024-03-14) — most recent
- Xiaozhen Fu (2024-03-14)
Cite as:
“Sparse subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sparse_subsystem