YQI Talk - Dongjin Lee - Perimeter Institute

Chiral Color Code: Single-shot error correction for exotic topological order and beyond.

In this talk, I will introduce a family of simple three-dimensional stabilizer codes, called the chiral color codes, that realize fermionic and chiral topological orders. In the qubit case, the code realizes the topological phase of a single copy of the fermionic toric code. For qudit systems with local dimension d, the model features a chiral parameter \alpha and realizes 3D topological phases characterized by Z_d^\alpha anyon theories with anomalous chiral surface topological order. Furthermore, we prove that the bulk is short-range entangled (for odd d, coprime \alpha) by constructing an explicit local quantum channel that prepares the ground state. The chiral color codes are constructed within the gauge color code, and hence inherit its fault-tolerant features: they admit single-shot error correction and allow code switching to other stabilizer color codes. These properties position the chiral color codes as particularly useful platforms for realizing and manipulating fermions and chiral anyons. In the last part of the talk, I will also explain chiral stabilizer mixed states that arise at the boundary of chiral color codes, which cannot be diagnosed by the either modular commutator or chiral central charge.