Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916882817220608 |
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| author | Iulianelli, Filippo Kim, Sung Sussan, Joshua Lauda, Aaron D. |
| author_facet | Iulianelli, Filippo Kim, Sung Sussan, Joshua Lauda, Aaron D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory Iulianelli, Filippo Kim, Sung Sussan, Joshua Lauda, Aaron D. Quantum Physics Strongly Correlated Electrons Quantum Algebra 81P68, 18M20, 57K16, 17B37, 81R50 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. |
| title | Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory |
| topic | Quantum Physics Strongly Correlated Electrons Quantum Algebra 81P68, 18M20, 57K16, 17B37, 81R50 |
| url | https://arxiv.org/abs/2410.14860 |