Schreiber Rethinking Topological Quantum Logic

An Ignite-style talk that I will have given:

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• Urs Schreiber:

  
  

  Rethinking Topological Quantum Logic

  
  

  talk at Softmax AI Alignment-meeting

  @ The Royal Institution

  London (22 May 2025)

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Exposition of:

• Engineering of Anyons on M5-Probes via Flux-Quantization

• Understanding Fractional Quantum Hall Systems via the Algebraic Topology of exotic Flux Quanta

Outline (preliminary):

I – Problem

• quantum computers excessively more powerful than classical ones — in principle

• possible dramatic enhancement for machine learning algorithms — in principle

• but quantum is immensely noise intolerant $\Rightarrow$ existing quantum computers are puny

• popular hope: live with the noise and fight it by software: “quantum error correction”

• more profound approach: prevent noise on hardware by fundamental physical effects!

• tantalizing candidate: topological quantum effects save information in knotted states

• but theoretical understanding remained superficial & experimental claims remain dubious

• because topological quantum is “non-perturbative physics”: a $1M “Millennium Problem”

II – Solution

• recent understanding @CQTS [LMP 115 36 (2025)] of engineering topological quantum on M-branes

• namely, topological states in “fractional quantum Hall systems carried by exotic magnetic flux quanta

• but state-of-the-art understanding of magnetic flux quantization was a century old [Dirac 1931]

• now novel math developed @CQTS [EoMP 4 (2025) 281] explains generalized exotic flux quantization

• shows$\;$there exists an exotic "flux quantization law" which knows fractional Hall quantum topology!

• this novel law (“Hypothesis H”) predicts pathway to topological quantum logic via “defect anyons”

• I [will have] just come from a meeting at ShabaniLab@NYU NY, discussing experimental prospects

$\Rightarrow\;$ gate opened towards scaling-up quantum computers & thus
$\phantom{\Rightarrow\;}$ towards practical quantum advantage in machine learning?

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