The symmetry of a quantum system can give rise to topologically distinct degenerate ground states. A quantum superposition of such states is, in principle, immune to dephasing; additionally, an energy gap separates the ground states torn the excited states and further protects the ground states from energy decay. As such, symmetry-protected ground states may form decoherence-free subspaces (1-4) and are promising candidates for topological quantum computing (5, 6). An example model supporting symmetry-protected topological states is the Kitaev model of spinless fermions in a one-dimensional (ID) wire (7). The Z_2 parity symmetry of the model leads to a pair of degenerate ground states. The distinct parities of the two ground stales protect them against local parity-preserving noise, such as potential fluctuations (8). The topological property of these degenerate ground states is commonly described by a pair of localized Majorana edge modes (MEMs) at the ends of the wire.
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