Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model

Abstract

Topological properties of quantum systems could provide protection of information against environmental noise, and thereby drastically advance their potential 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. Here, we propose and study 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 zeroenergy modes. With numerical simulations, we demonstrate that the gate is robust against hopping disorder but is corrupted by disorder in the on-site energy. Then we show that this robustness is topological protection, and that it arises as a joint consequence of chiral symmetry, time-reversal symmetry and the spatial separation of the zero-energy modes bound to the defects. This setup will most likely not lead to a practical quantum computer, nevertheless it does provide valuable insight to aspects of 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. arXiv:1902.01358v2 [cond-mat.mes-hall]

Topological Braiding of Non-Abelian Midgap Defects in Classical Metamaterials

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Tunable zero modes and quantum interferences in flat-band topological insulators

“…where δJ is the level of disorder, t c i is the value of the amplitude in a clean system, and R is a uniformly drawn random number between −1/2 and 1/2, chosen individually for each term in the Hamiltonian and for each value of δJ. The level of disorder ranges from zero to ξ (with ξ = 1) to better appreciate its effects, but it must be noted that the level of disorder expected in a real experimental setup would be much smaller, on the order of 0.1ξ [2,3,6].…”

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