Universal topological phase of 2D stabilizer codes

TL;DR

This paper demonstrates that all 2D topological stabilizer codes are fundamentally equivalent to multiple copies of Kitaev's topological code, unifying their classification and aiding error correction.

Contribution

It establishes a universal topological phase for 2D stabilizer codes, simplifying their classification and linking them to Kitaev's code.

Findings

All 2D topological stabilizer codes are equivalent to multiple copies of Kitaev's code.

The universal phase facilitates understanding of long-range entanglement patterns.

Local mappings improve error correction strategies.

Abstract

Two topological phases are equivalent if they are connected by a local unitary transformation. In this sense, classifying topological phases amounts to classifying long-range entanglement patterns. We show that all 2D topological stabilizer codes are equivalent to several copies of one universal phase: Kitaev's topological code. Error correction benefits from the corresponding local mappings.