Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
H. Bombin
TL;DR
This paper demonstrates that color codes possess an optimal set of transversal gates determined solely by spatial dimension, introduces a subsystem version, and enables universal gates via gauge fixing in 3D.
Contribution
It establishes the optimality of transversal gates in color codes and introduces a subsystem variant that facilitates universal quantum computation through gauge fixing.
Findings
Transversal gates depend only on spatial dimension.
Subsystem color codes enable universal gates in 3D.
Error detection involves only 4 or 6 qubits.
Abstract
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a generalized, subsystem version of color codes. In 3D they allow the transversal implementation of a universal set of gates by gauge fixing, while error-detecting measurements involve only 4 or 6 qubits.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Error Correcting Code Techniques · Quantum Computing Algorithms and Architecture