Quantum multi-dimensional parity-check (QMDPC) code[1]
Description
High-rate low-distance CSS code whose qubits lie on a \(D\)-dimensional rectangle, with \(X\)-type stabilizer generators defined on each \(D-1\)-dimensional rectangle. The \(Z\)-type stabilizer generators are defined via permutations in order to commute with the \(X\)-type generators.
For example, the \(D=2\) square geometry corresponds to a \([[n^2,n^2-4n+2,4]]\) code, with \(X\)-type stabilizer generators defined on rows and columns.
Protection
The general construction for a \(D\)-dimensional rectangle with sides \(n_i\) yields a \([[\prod_{i=1}^{D}n_{i},2\prod_{i=1}^{D}(n_{i}-1)-\prod_{i=1}^{D}n_{i},2^{D}]]\) code family.Cousins
- Yoked surface code— Yoked surface codes are concatenations of QMDPC codes with rotated surface codes.
- Small-distance qubit stabilizer code— QMDPC codes for dimensions \(D \leq 2\) are examples of small distance qubit stabilizer codes.
Member of code lists
Primary Hierarchy
Parents
Quantum multi-dimensional parity-check (QMDPC) code
Children
The \([[2m,2m-2,2]]\) error-detecting code is a 1D QMDPC.
References
- [1]
- C. Gidney, M. Newman, P. Brooks, and C. Jones, “Yoked surface codes”, (2023) arXiv:2312.04522
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2023-12-08)
Cite as:
“Quantum multi-dimensional parity-check (QMDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/qmdpc, arXiv:2606.11484