dorsal/arxiv
View SchemaTopological Quantum Computation
| Authors | Michael H. Freedman, Alexei Kitaev, Michael J. Larsen, Zhenghan Wang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101025 |
| URL | https://arxiv.org/abs/quant-ph/0101025 |
Abstract
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possibility for the realization of quantum computers. The chief advantage of anyonic computation would be physical error correction: An error rate scaling like $e^{-\a\l}$, where $\l$ is a length scale, and $\alpha$ is some positive constant. In contrast, the $\q$presumptive" qubit-model of quantum computation, which repairs errors combinatorically, requires a fantastically low initial error rate (about $10^{-4}$) before computation can be stabilized.
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"abstract": "The theory of quantum computation can be constructed from the abstract study\nof anyonic systems. In mathematical terms, these are unitary topological\nmodular functors. They underlie the Jones polynomial and arise in\nWitten-Chern-Simons theory. The braiding and fusion of anyonic excitations in\nquantum Hall electron liquids and 2D-magnets are modeled by modular functors,\nopening a new possibility for the realization of quantum computers. The chief\nadvantage of anyonic computation would be physical error correction: An error\nrate scaling like $e^{-\\a\\l}$, where $\\l$ is a length scale, and $\\alpha$ is\nsome positive constant. In contrast, the $\\q$presumptive\" qubit-model of\nquantum computation, which repairs errors combinatorically, requires a\nfantastically low initial error rate (about $10^{-4}$) before computation can\nbe stabilized.",
"arxiv_id": "quant-ph/0101025",
"authors": [
"Michael H. Freedman",
"Alexei Kitaev",
"Michael J. Larsen",
"Zhenghan Wang"
],
"categories": [
"quant-ph",
"math.GT"
],
"title": "Topological Quantum Computation",
"url": "https://arxiv.org/abs/quant-ph/0101025"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e21af527-82c1-4677-a90c-2d90c2985dbc",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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