Alternative names: Sparse subsystem code.
Description
Member of a family of subsystem stabilizer codes for which the number of sites participating in each gauge generator and the number of gauge generators that each site participates in are both bounded by a constant as \(n\to\infty\). The stabilizer group may contain generators of unbounded weight, distinguishing these codes from stabilizer codes with bounded-weight generators for which some logical qubits were re-assigned to be gauge qubits.Rate
There exists a family of QLDPC subsystem codes with \(d = n^{1-\epsilon}\), where \(\epsilon = O(1/\sqrt{\log n})\) [1]. Spatially local subsystem codes also exist in \(D\geq 2\) dimensions with \(d = n^{1-\epsilon-1/D}\), where \(\epsilon = O(1/\sqrt{\log n})\), nearly saturating the subsystem BT bound [1].Cousins
- QLDPC code— QLDPC subsystem codes reduce to QLDPC codes when there are no gauge degrees of freedom.
- Qubit QLDPC code— Any qubit QLDPC code with stabilizer-generator weights \(w_i\) can be mapped constructively to a sparse subsystem qubit code with the same number of logical qubits and distance, using \(n=O(\sum_i w_i)\) physical qubits and constant-weight gauge generators [1].
Primary Hierarchy
Parents
QLDPC subsystem code
Children
Lattice subsystem codes are QLDPC subsystem codes that are defined on Euclidean lattices.
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:
“QLDPC subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sparse_subsystem