Non Abelian Anyon Proliferation Stat Mech

---
name: non-abelian-anyon-proliferation-stat-mech
description: Statistical mechanics and symmetry methodology for analyzing stability of non-Abelian topological order under wavefunction deformations and decoherence. Maps topological order instability to stat-mech models whose symmetries expose corrupting anyonic excitations.
category: quantum-topology
tags: [topological-quantum-computation, non-abelian-anyons, statistical-mechanics, symmetry-analysis, decoherence, monte-carlo, quantum-error-correction]
created: 2026-06-12
source: arXiv:2606.12527 - Vadali, Vanhove, Verresen, Alicea, Sala (2026)
---

# Non-Abelian Anyon Proliferation via Statistical Mechanics

## Overview
Methodology for analyzing the stability of topological quantum computation by mapping the instability of topological order to wavefunction deformations and environmental noise into statistical mechanics models. The symmetries of these stat-mech models naturally expose the corrupting anyonic excitations.

## Core Methodology

### 1. Stat-Mech Model Mapping
- Map topological order instability under:
  - Wavefunction deformations (imperfect state preparation)
  - Decoherence (environmental noise probed by syndrome distributions)
- Result: stat-mech models whose symmetries reveal corrupting anyonic excitations

### 2. Non-Abelian Anyon Proliferation Analysis
- Use Monte-Carlo simulations to resolve stability
- Example: D₄ topological order under deformations and quantum channels
- Multiple non-Abelian anyon species that individually cannot condense

### 3. Parasitic Condensation Threshold
- Beyond finite threshold, proliferation of two non-Abelian anyon species
- Parasitically condenses a shared Abelian-anyon fusion outcome
- Destroys the topological order

### 4. Symmetry-Based Phase Differentiation
- Symmetry approach distinguishes resulting trivial phase from condensing all Abelian charges
- The trivial phase "remembers" which anyons condensed
- Provides framework for identifying relevant symmetry for optimal decoders

## Key Techniques
- Monte-Carlo simulations for topological order stability
- Symmetry analysis of stat-mech models
- Syndrome distribution analysis for decoherence probing
- Anyon fusion outcome tracking

## Applications
- Topological quantum computation stability analysis
- Non-Abelian anyon-based quantum error correction
- Decoder design conditioned on syndrome measurements
- Phase transition analysis in topological order

## Trigger Words
non-abelian anyon, topological order, statistical mechanics, anyon proliferation, decoherence, syndrome distribution, D4 topological order, Monte-Carlo, parasitic condensation, quantum decoder