Subsystem Hypergraph Product Simplex (SHYPS) code[1]
Description
A member of the family of \([(2^r − 1)^2, r^2, 2^{r−1}]\) SHP codes for \(r \geq 3\) with weight-three gauge generators constructed from a hypergraph product of simplex codes.
Their automorphism group is \(GL_{r}(\mathbb{F}_2)\), inherited from the automorphism group of the simplex codes.
Transversal Gates
Fold-transversal Hadamard gate on all logical qubits and various phase-type gates [1].Gates
Roughly \(4m\) cycles of depth-one physical Clifford operations followed by syndrome extraction yield arbitrary \(m\)-qubit logical Clifford gates [1].Logical Clifford operation on \(b\) blocks can be implemented fault-tolerantly in depth roughly \(4b r^2\) [1].Fault Tolerance
Logical Clifford operation on \(b\) blocks can be implemented fault-tolerantly in depth roughly \(4b r^2\) [1].Cousin
- \([2^m-1,m,2^{m-1}]\) simplex code— SHYPS code gauge generator matrices are constructed from hypergraph products of simplex codes [1].
Primary Hierarchy
Parents
Subsystem Hypergraph Product Simplex (SHYPS) code
References
- [1]
- A. J. Malcolm et al., “Computing Efficiently in QLDPC Codes”, (2025) arXiv:2502.07150
Page edit log
- Victor V. Albert (2025-03-14) — most recent
Cite as:
“Subsystem Hypergraph Product Simplex (SHYPS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/shyps