Topological Quantum Compiling

Abstract

A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.

20 pages, 20 figures, published version

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Cited by in corpus (63)

• Non-Abelian Anyons and Topological Quantum Computation
• From Luttinger liquid to non-Abelian quantum Hall states
• Introduction to topological quantum computation with non-Abelian anyons
• Quantum computation with Turaev-Viro codes
• Interferometry of non-Abelian Anyons
• Asymptotically Optimal Topological Quantum Compiling
• Topological Quantum Compiling with Reinforcement Learning
• Superconducting analogue of the parafermion fractional quantum Hall states
• Mosaic spin models with topological order
• Topological Quantum Computing with Read-Rezayi States
• Topological Qubit Design and Leakage
• Non-Abelian Braiding of Lattice Bosons
• Resources Required for Topological Quantum Factoring
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• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
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• Mapping the braiding properties of the Moore-Read state
• Quantum Circuits for Measuring Levin-Wen Operators
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
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