Classification of two-dimensional quantum systems with Z3-graded topological symmetries

Z Wang

Keivan Aghababaei Samani, Davood Pooladsaz

In this paper we consider $Z_3$-graded topological symmetries (TSs) in one dimensional quantum mechanics. We give a classification of one dimensional quantum systems possessing these symmetries and show that different classes correspond to a positive integer $N$.

Antônio Sérgio Teixeira Pires

Yuxuan Zhang, Weitong Hu, Wei Zhang

Current quantum computing platforms, primarily based on Z2-graded qubits, suffer from fragility against decoherence and limited error correction thresholds. Here, we propose a topological quantum computing architecture founded on the finite-dimensional 19-dimensional Z3-graded Lie superalgebra and its emergent discrete 44-vector vacuum lattice—a minimal, closed geometric realization of ternary symmetry in 3D embedding space. The lattice supports stable non-Abelian anyonic excitations encoded as native qutrits, with triality-protected braiding offering intrinsic topological error correction and enhanced coherence times. We derive universal gate operations from graded bracket closure, estimate fault-tolerance thresholds exceeding 1.5% noise (significantly surpassing conventional surface code thresholds of ∼0.7–1%), and outline near-term experimental pathways in photonic lattices, cold atoms, and superconducting circuits. This Z3 framework provides a promising candidate for scalable, decoherenceresistant quantum computation, potentially resolving current bottlenecks in qubit-based platforms while bridging algebraic unification with practical quantum hardware.

Yunqing Ouyang, Qing-Rui Wang, Zheng‐Cheng Gu +1 more

Hrant Topchyan, Vasilii Iugov, Mkhitar Mirumyan +3 more

Abstract We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by (×Z3)3 ≡ Z3 × Z3 × Z3 symmetry and smaller Z3 symmetry. We derive microscopic models for the gapless edge, uncover their symmetries and analyze the conformal properties. We study the properties of the gapless edge by employing the numerical density-matrix renormalization group (DMRG) simulation and exact diagonalization. We discuss the corresponding conformal field theory, its central charge, and the scaling dimension of the corresponding primary field. We argue, that the low energy limit of our edge modes defined by the SUk(3)/SUk(2) coset conformal field theory with the level k = 2. The discussed two-dimensional models realize a variety of symmetry-protected topological phases, opening a window for studies of the unconventional quantum criticalities between them.