Schreiber Homotopy Theory for Topological Quantum Computing

A talk that we will have given:

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• Hisham Sati$\;$and$\;$ Urs Schreiber:

  
  

  Homotopy Theory for Topological Quantum Computing

  
  

  talk at:

  4th International Conference on Mathematics and Statistics

  American University of Sharjah, 20-22 Feb 2025

  
  

  talk notes: [to appear here]

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Abstract: While topological quantum hardware is expected to be controlled by the mathematics of braided fusion categories, little attention has been paid to a more first-principles understanding of this phenomenon. We will survey recent advances [1,2,3] via “geometric engineering” that make crucial use of low-dimensional geometric homotopy theory for “flux quantization” [4].

Based on:

[1] Abelian Anyons on Flux-Quantized M5-Branes

[2] Anyons on M5-Probes of Seifert 3-Orbifolds

[3] Engineering of Anyons on M5-Probes (lecture notes)

[4] Flux Quantization