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  • Open Access

Chiral Color Code: Single-Shot Error Correction for Exotic Topological Order

Dongjin Lee1,2,* and Beni Yoshida1,†

  • *Contact author: dlee@perimeterinstitute.ca
  • †Contact author: byoshida@perimeterinstitute.ca
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PRX Quantum 7, 033015 – Published 21 July, 2026

DOI: https://doi.org/10.1103/sqcs-jk1z

Abstract

We present 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 α and realizes 3D topological phases characterized by Zd(α) anyon theories with anomalous chiral surface topological order. On closed manifolds, the code has a unique ground state after removing bulk transparent fermions or bosons. Furthermore, we prove that the bulk is short-range entangled (for odd d, coprime α) 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.

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Popular Summary

In this work, we introduce the chiral color code, a simple three-dimensional quantum error-correcting code. Despite the model’s simplicity, it features strong fault-tolerance properties such as “single-shot quantum error correction,” meaning that a few rounds of noisy measurements are enough to protect the quantum information encoded in this code. These properties can significantly reduce the time cost for quantum computation. What makes the code more exciting is the kind of quantum phases it can realize. Beyond the familiar toric code type models, which have been well explored in the quantum information community, our model hosts a variety of exotic phases where particle-like excitations behave as fermions or chiral anyons. Due to the simplicity of our model, we could also explicitly confirm a long-standing belief in the condensed matter community that the bulk state of this type of phase should be short-range entangled after removing transparent particles, within a unified footing. Practically, the chiral color code can bridge between standard quantum computing architectures based on bosonic degrees of freedom (spins) and the platforms that use fermionic or chiral degrees of freedom. Thus, it may open novel routes to protect quantum information and implement fault-tolerant logical gates. The chiral color code also connects to an alternative quantum computation paradigm, known as measurement-based quantum computing, through underlying higher-form symmetries, suggesting it can serve as a fault-tolerant resource state.

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PRX Quantum 7, 033015– Published 21 July, 2026
  • Received 12 December 2025
  • Accepted 14 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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