Topological properties of quantum systems could provide protection of the encoded quantum information against environmental noise, and thereby drastically advance the potential of these setups in quantum information processing. Most proposals for topologically protected quantum gates are based on many-body systems, e.g., fractional quantum Hall states, exotic superconductors, or ensembles of interacting spins, bearing an inherent conceptual complexity. In this talk, I will propose and discuss a topologically protected quantum gate, based on a one-dimensional single-particle tight-binding model, known as the Su-Schrieffer-Heeger chain. The proposed Y gate acts in the two-dimensional zero-energy subspace of a Y junction assembled from three chains, and is based on the spatial exchange of the defects supporting the zero-energy modes. Using numerical results, I will demonstrate that the gate is robust against hopping disorder but is corrupted by disorder in the on-site energy. Then I will argue that this robustness is topological protection. This setup will most likely not lead to a practical quantum computer, nevertheless it does provide valuable insight to topological quantum computing as an elementary minimal model. Since this model is non-interacting and non-superconducting, its dynamics can be studied experimentally, e.g., using coupled optical waveguides.
Reference: Péter Boross, János K. Asbóth, Gábor Széchenyi, László Oroszlány, András Pályi, https://arxiv.org/abs/1902.01358