Description
An \([m+Dm,Dm,3]\) linear binary code for \(m\geq 3^D\), defined by the Gauss' law constraint of a \(D\)-dimensional fermionic \(\mathbb{Z}_2\) gauge theory [2; Thm. 1]. The code can be re-phrased as a distance-one stabilizer code whose stabilizers consist of gauge-group elements. It can be concatenated to form a stabilizer code for fault-tolerant quantum simulation of the underlying gauge theory [1,2].Cousins
- Abelian topological code— Gauge-group elements of a \(D\)-dimensional fermionic \(\mathbb{Z}_2\) gauge theory form a single-error-correcting linear binary code [2; Thm. 1]. There is a general correspondence between stabilizer codes and gauge theory, with the stabilizer group playing the role of the gauge group [3], and with the Gauss' law code being a specific example.
- Fermion-into-qubit code— Gauge-group elements of a \(D\)-dimensional fermionic \(\mathbb{Z}_2\) gauge theory form a single-error-correcting linear binary code [2; Thm. 1].
- Concatenated qubit code— The Gauss' law code can be concatenated to form a stabilizer code for fault-tolerant quantum simulation of the underlying gauge theory [1,2].
Member of code lists
Primary Hierarchy
References
- [1]
- A. Rajput, A. Roggero, and N. Wiebe, “Quantum Error Correction with Gauge Symmetries”, (2022) arXiv:2112.05186
- [2]
- L. Spagnoli, A. Roggero, and N. Wiebe, “Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes”, (2024) arXiv:2405.19293
- [3]
- S. Carrozza, A. Chatwin-Davies, P. A. Hoehn, and F. M. Mele, “A correspondence between quantum error correcting codes and quantum reference frames”, (2024) arXiv:2412.15317
Page edit log
- Victor V. Albert (2024-07-10) — most recent
Cite as:
“Gauss' law code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/gauss_law