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

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...

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Bibliographic Details
Published in:Physical review. B 2019-07, Vol.100 (4), p.045414, Article 045414
Main Authors: Boross, Péter, Asbóth, János K., Széchenyi, Gábor, Oroszlány, László, Pályi, András
Format: Article
Language:English
Subjects:
Background noise
Chains
Computer simulation
Data processing
Defects
Mathematical models
Optical waveguides
Quantum computers
Quantum computing
Quantum phenomena
Robustness (mathematics)
Superconductor junctions
Superconductors
Symmetry
Topology
Y junctions
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Summary: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 zero-energy 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 noninteracting and nonsuperconducting, its dynamics can be studied experimentally, e.g., using coupled optical waveguides.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.100.045414