dorsal/arxiv
View SchemaA modular functor which is universal for quantum computation
| Authors | Michael Freedman, Michael Larsen, Zhenghan Wang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001108 |
| URL | https://arxiv.org/abs/quant-ph/0001108 |
Abstract
We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern-Simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model. The chief technical advance: the density of the irreducible sectors of the Jones representation, have topological implications which will be considered elsewhere.
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"date_created": "2026-03-02T18:01:35.813000Z",
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"abstract": "We show that the topological modular functor from Witten-Chern-Simons theory\nis universal for quantum computation in the sense a quantum circuit computation\ncan be efficiently approximated by an intertwining action of a braid on the\nfunctor\u0027s state space. A computational model based on Chern-Simons theory at a\nfifth root of unity is defined and shown to be polynomially equivalent to the\nquantum circuit model. The chief technical advance: the density of the\nirreducible sectors of the Jones representation, have topological implications\nwhich will be considered elsewhere.",
"arxiv_id": "quant-ph/0001108",
"authors": [
"Michael Freedman",
"Michael Larsen",
"Zhenghan Wang"
],
"categories": [
"quant-ph",
"math.GT"
],
"title": "A modular functor which is universal for quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0001108"
},
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