Protocols for Creating Anyons and Defects via Gauging

2024/11/06 by Alex Lyons, Lyons, Anasuya, Chi‐Fai Lo +7 · 3 citations
Engineering · #Manufacturing Process and Optimization

paper · pdf · doi:10.48550/arxiv.2411.04181

Abstract

Creating and manipulating anyons and symmetry defects in topological phases, especially those with a non-Abelian character, constitutes a primitive for topological quantum computation. We provide a physical protocol for implementing the ribbon operators of non-Abelian anyons and symmetry defects. We utilize dualities, in particular the Kramers-Wannier or gauging map, which have previously been used to construct topologically ordered ground states by relating them to simpler states. In this work, ribbon operators are implemented by applying a gauging procedure to a lower-dimensional region of such states. This protocol uses sequential unitary circuits or, in certain cases, constant-depth adaptive circuits. We showcase this for anyons and defects in the ℤ₃ toric code and S₃ quantum double. The general applicability of our method is demonstrated by deriving unitary expressions for ribbon operators of various (twisted) quantum doubles.

Cited by

• Universal Gates from Braiding and Fusing Anyons on Quantum Hardware
• Bridging Microscopic Constructions and Continuum Topological Field Theory of Three-Dimensional Non-Abelian Topological Order
• Non-abelian quantum double models from iterated gauging

Related

• Universal Quantum Computation with the S₃ Quantum Double: A Pedagogical Exposition
• Symmetry defects and their application to topological quantum computing
• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• Quantum Field Theories, Topological Materials, and Topological Quantum Computing
• Quantum Computing with ℤ₂ Abelian anyon system