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arXiv:1705.06206math.QA

Mathematics of Topological Quantum Computing

Eric C. Rowell, Zhenghan Wang

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Abstract

In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by experiments to an accuracy of $10^{-10}$, and harnessed to stabilize quantum memory. In this survey, we discuss the conceptual development of this interdisciplinary field at the juncture of mathematics, physics and computer science. Our focus is on computing and physical motivations, basic mathematical notions and results, open problems and future directions related to and/or inspired by topological quantum computing.

arXiv comments
51 pages, 8 figures, 1 table. Version 2: reorganized, typos fixed, explanations added
Journal reference
DOI
Subjects
math.QAQuantum Algebra cond-mat.str-elStrongly Correlated Electrons math-phMathematical Physics quant-phQuantum Physics

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Linked by 1 identifiable commenter in 1 comment across 1 thread, from May 2017 to May 2017. Found in 1 HN submission from May 2017 to May 2017. Open submission discussions.

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  1. Introduction to Topological Quantum Computation 1 comment

    • Alternatively "Mathematics of Topological Quantum Computing" Eric C. Rowell, Zhenghan Wang https://arxiv.org/abs/1705.06206

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