Fibonacci Anyons Versus Majorana Fermions: A Monte Carlo Approach to the Compilation of Braid Circuits in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>k</mml:mi></mml:msub></mml:math> Anyon Models
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