Authors:

Tayden Aris White

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About Paper:

Anyons are point-like, particle-like excitations that can arise in (2+1)- dimensional quantum systems called topological phases of matter. Permutation defects are similar point-like objects that can arise when there are multiple layers hosting the same anyons stacked on top of each other. The name "permutation defect" comes from the symmetry that permutes the identical layers of the total system. The interactions of these quasiparticles and defects are important to the emerging field of topological quantum computing. The fusion of permutation defects, in which two defects combine to form new ones, is modeled mathematically by an algebraic structure called a fusion ring. An algorithm for this fusion process has been described by my mentor Dr. Colleen Delaney, centering around the annihilation of so-called transposition defects, which form the building blocks of more general permutation defects in the same way that any permutation of objects can be built up from pairwise exchanges, or transpositions. In this project, I work to understand and explain the time complexity of this algorithm. I will show that this is an efficient method for computing the fusion of permutation defects and implement the algorithm using computer algebra software. Keywords: Permutation Defect; Time Complexity; Algorithm; Anyons

Source:

Purdue University / 2025

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Co-authors:

Tayden Aris White