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].
Parents
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].
- 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].
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
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