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arXiv · 1609.02037

Topological Quantum Computation with Gapped Boundaries

Iris Cong·Meng Cheng·Zhenghan Wang
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Abstract

This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also provide a commuting Hamiltonian to realize defects between boundaries in any quantum double model. Next, we present the algebraic/categorical structure of gapped boundaries and boundary defects, which will be used to describe topologically protected operations and obtain quantum gates. To demonstrate a potential physical realization, we provide quantum circuits for surface codes that can perform all basic operations on gapped boundaries. Finally, we show how gapped boundaries of the abelian theory $\mathfrak{D}(\mathbb{Z}_3)$ can be used to perform universal quantum computation.

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BibTeXRIS

Iris Cong, Meng Cheng, Zhenghan Wang. 2016-09-07. Topological Quantum Computation with Gapped Boundaries. https://arxiv.org/abs/1609.02037

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