2024/10/18 by Filippo Iulianelli, Iulianelli, Filippo, Sung Wng Kim +5 · 4 citations
Computer Science · Physics and Astronomy · #17B37 #18M20 #57K16 #81P68 #81R50 #FOS: Mathematics #FOS: Physical sciences #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2410.14860
openalex publication_date 2024/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced theories offer more powerful models for quantum computation. The conventional theory of Ising anyons, which is believed to describe excitations in the ν= 5/2 fractional quantum Hall state, is not universal for quantum computation via braiding of quasiparticles. However, we show that the non-semisimple theory introduces new anyon types that extend the Ising framework. By adding just one new anyon type, universal quantum computation can be achieved through braiding alone. This result opens new avenues for realizing fault-tolerant quantum computing in topologically ordered systems.