It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful quantum error correction. At the same time, the promise of using general topological orders for practical error correction remains largely unfulfilled to date. In this work, we significantly contribute to establishing such a connection by showing that Abelian twisted quantum double models can be used for quantum error correction. By exploiting the group cohomological data sitting at the heart of these lattice models, we transmute the terms of these Hamiltonians into full-rank, pairwise commuting operators, defining commuting stabilizers. The resulting codes are defined by non-Pauli commuting stabilizers, with local systems that can either be qubits or higher dimensional quantum systems. Thus, this work establishes a new connection between condensed matter physics and quantum information theory, and constructs tools to systematically devise new topological quantum error correcting codes beyond toric or surface code models.
 Antonio Acín, Immanuel Bloch, Harry Buhrman, Tommaso Calarco, Christopher Eichler, Jens Eisert, Daniel Esteve, Nicolas Gisin, Steffen J Glaser, Fedor Jelezko, and et al. The quantum technologies roadmap: a european community view. New Journal of Physics, 20 (8): 080201, Aug 2018. ISSN 1367-2630. 10.1088/1367-2630/aad1ea.
 Ruben S. Andrist, James R. Wootton, and Helmut G. Katzgraber. Error thresholds for abelian quantum double models: Increasing the bit-flip stability of topological quantum memory. Phys. Rev. A, 91: 042331, Apr 2015. 10.1103/PhysRevA.91.042331.
 H Bombin, Guillaume Duclos-Cianci, and David Poulin. Universal topological phase of two-dimensional stabilizer codes. New Journal of Physics, 14 (7): 073048, jul 2012. 10.1088/1367-2630/14/7/073048.
 Sergey Bravyi and Barbara Terhal. A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes. New Journal of Physics, 11 (4): 043029, apr 2009. 10.1088/1367-2630/11/4/043029.
 Earl T. Campbell. Enhanced fault-tolerant quantum computing in $d$-level systems. Phys. Rev. Lett., 113: 230501, Dec 2014. 10.1103/PhysRevLett.113.230501.
 Xie Chen. Symmetry fractionalization in two dimensional topological phases. Reviews in Physics, 2: 3–18, 2017. ISSN 2405-4283. https://doi.org/10.1016/j.revip.2017.02.002.
 Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen. Symmetry protected topological orders and the group cohomology of their symmetry group. Phys. Rev. B, 87: 155114, Apr 2013. 10.1103/PhysRevB.87.155114.
 G Dauphinais, L Ortiz, S Varona, and M A Martin-Delgado. Quantum error correction with the semion code. New Journal of Physics, 21 (5): 053035, may 2019. 10.1088/1367-2630/ab1ed8. URL https://doi.org/10.1088/1367-2630/ab1ed8.
 Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill. Topological quantum memory. Journal of Mathematical Physics, 43 (9): 4452–4505, 2002. 10.1063/1.1499754.
 Joydip Ghosh, Austin G. Fowler, and Michael R. Geller. Surface code with decoherence: An analysis of three superconducting architectures. Phys. Rev. A, 86: 062318, Dec 2012. 10.1103/PhysRevA.86.062318.
 Yuting Hu, Yidun Wan, and Yong-Shi Wu. Twisted quantum double model of topological phases in two dimensions. Phys. Rev. B, 87: 125114, Mar 2013. 10.1103/PhysRevB.87.125114.
 Markus S. Kesselring, Fernando Pastawski, Jens Eisert, and Benjamin J. Brown. The boundaries and twist defects of the color code and their applications to topological quantum computation. Quantum, 2: 101, October 2018. ISSN 2521-327X. 10.22331/q-2018-10-19-101.
 Alexei Kitaev. Anyons in an exactly solved model and beyond. Annals of Physics, 321 (1): 2–111, 2006. ISSN 0003-4916. 10.1016/j.aop.2005.10.005. January Special Issue.
 A.Yu. Kitaev. Fault-tolerant quantum computation by anyons. Annals of Physics, 303 (1): 2–30, 2003. ISSN 0003-4916. 10.1016/S0003-4916(02)00018-0.
 Aleksander Kubica, Beni Yoshida, and Fernando Pastawski. Unfolding the color code. New Journal of Physics, 17 (8): 083026, aug 2015. 10.1088/1367-2630/17/8/083026.
 Michael Levin and Zheng-Cheng Gu. Braiding statistics approach to symmetry-protected topological phases. Phys. Rev. B, 86: 115109, Sep 2012. 10.1103/PhysRevB.86.115109.
 Michael A. Levin and Xiao-Gang Wen. String-net condensation: A physical mechanism for topological phases. Phys. Rev. B, 71: 045110, Jan 2005. 10.1103/PhysRevB.71.045110.
 M. A. Nielsen and I. Chuang. Quantum computation and quantum information. Cambridge University Press, 2010.
 S. Varona and M. A. Martin-Delgado. Determination of the semion code threshold using neural decoders. Phys. Rev. A, 102: 032411, Sep 2020. 10.1103/PhysRevA.102.032411.
 S. Varona and M. A. Martin-Delgado, "Determination of the semion code threshold using neural decoders", Physical Review A 102 3, 032411 (2020).
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