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The recent "honeycomb code" is a fault-tolerant quantum memory defined by a sequence of checks which implements a nontrivial automorphism of the toric code.
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Lukasz Fidkowski, Hoi Chun Po, Andrew C Potter, and Ashvin Vishwanath, “Interacting invariants for floquet phases of fermions in two dimensions,” Physical Review B 99
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Alexei Kitaev, “Conclusion: Toward a topological classification of many-body quantum states with short-range entanglement,” (2011b), Talk at Simons Center for Geometry and Physics
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Michael Freedman, Jeongwan Haah, and Matthew B Hastings, “The group structure of quantum cellular automata,” Communications in Mathematical Physics , 1–26 (2022)
2022
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Laurens Lootens, Bram Vancraeynest-De Cuiper, Norbert Schuch, and Frank Verstraete, “Mapping between morita-equivalent string-net states with a constant depth quantum circuit,” Phys. Rev. B 105
2022
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