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Protocols for Creating Anyons and Defects via Gauging.

Anasuya Lyons1, Chiu Fan Bowen Lo1, Nathanan Tantivasadakarn2

  • 1Harvard University, Department of Physics, Cambridge, Massachusetts 02138, USA.

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|November 30, 2025
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Summary
This summary is machine-generated.

This study introduces a physical protocol for creating and manipulating non-Abelian anyons and symmetry defects, crucial for topological quantum computation. The method uses dualities and gauging procedures to implement ribbon operators in topological phases.

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Area of Science:

  • Quantum Physics
  • Condensed Matter Physics
  • Quantum Information Science

Background:

  • Topological phases of matter host exotic particles called anyons.
  • Non-Abelian anyons are essential for topological quantum computation due to their unique braiding properties.
  • Symmetry defects in topological phases also play a critical role in quantum information processing.

Purpose of the Study:

  • To provide a practical physical protocol for implementing ribbon operators of non-Abelian anyons and symmetry defects.
  • To demonstrate the utility of dualities, specifically the Kramers-Wannier map, in constructing topological states and their operators.
  • To offer a method applicable to various topological phases, including the Z3 toric code and S3 quantum double.

Main Methods:

  • Utilizing dualities (Kramers-Wannier map/gauging) to relate complex topological states to simpler ones.
  • Implementing ribbon operators by applying a gauging procedure to lower-dimensional regions of topological states.
  • Employing sequential unitary circuits or constant-depth adaptive circuits for operator implementation.

Main Results:

  • A concrete physical protocol for implementing ribbon operators of non-Abelian anyons and symmetry defects is presented.
  • The protocol is successfully demonstrated for anyons and defects in the Z3 toric code and S3 quantum double.
  • Unitary expressions for ribbon operators in various (twisted) quantum doubles are derived, showcasing the method's general applicability.

Conclusions:

  • The developed protocol offers a viable pathway for creating and manipulating essential elements for topological quantum computation.
  • The use of dualities and gauging provides an efficient route to engineer complex topological phenomena.
  • This work advances the practical realization of topological quantum computing primitives.