Plaquette Ising code

Plaquette Ising code[1–3]

Alternative names: Right-angle water ice code, Xu-Moore code.

Classical code defined on a two-dimensional square lattice whose parity checks are applied on the four vertices of each square.

The code has parameters \([L^2,2L-1,L]\) on a square lattice of size \(L\) [4].

Rotated surface code— The plaquette Ising model can be thought of as the rotated surface code whose \(X\)-type stabilizer generators have been converted to \(Z\)-type stabilizer generators.
Two-foliated fracton code— The two-foliated fracton code is a hypergraph product of the repetition code and the plaquette Ising code on a square lattice with periodic boundary conditions [4].

Parents

Plaquette Ising code

[1]: Ziman, John M. Models of disorder: the theoretical physics of homogeneously disordered systems. Cambridge university press, 1979.
[2]: J. E. Moore and D.-H. Lee, “Geometric effects onT-breaking inp+ipandd+idsuperconducting arrays”, Physical Review B 69, (2004) arXiv:cond-mat/0309717 DOI
[3]: C. Xu and J. E. Moore, “Strong-Weak Coupling Self-Duality in the Two-Dimensional Quantum Phase Transition ofp+ipSuperconducting Arrays”, Physical Review Letters 93, (2004) arXiv:cond-mat/0312587 DOI
[4]: N. P. Breuckmann, M. Davydova, J. N. Eberhardt, and N. Tantivasadakarn, “Cups and Gates I: Cohomology invariants and logical quantum operations”, (2024) arXiv:2410.16250

Page edit log

“Plaquette Ising code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/plaquette_ising