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].Cousin
- Quantum LDPC (QLDPC) code— Sparse subsystem codes reduce to QLDPC codes when there are no gauge qudits.
Member of code lists
Primary Hierarchy
Parents
Sparse subsystem code
Children
Lattice subsystem codes are sparse subsystem codes on Euclidean geometries.
References
- [1]
- D. Bacon, S. T. Flammia, A. W. Harrow, and J. Shi, “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