dorsal/arxiv
View SchemaSimulation of topological field theories by quantum computers
| Authors | Michael H. Freedman, Alexei Kitaev, Zhenghan Wang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001071 |
| URL | https://arxiv.org/abs/quant-ph/0001071 |
| DOI | 10.1007/s002200200635 |
| Journal | Commun.Math.Phys. 227 (2002) 587-603 |
Abstract
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned topological models having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H = 0. These are called topological quantum filed theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold: 1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model BQP. 2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm.
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"abstract": "Quantum computers will work by evolving a high tensor power of a small (e.g.\ntwo) dimensional Hilbert space by local gates, which can be implemented by\napplying a local Hamiltonian H for a time t. In contrast to this quantum\nengineering, the most abstract reaches of theoretical physics has spawned\ntopological models having a finite dimensional internal state space with no\nnatural tensor product structure and in which the evolution of the state is\ndiscrete, H = 0. These are called topological quantum filed theories (TQFTs).\nThese exotic physical systems are proved to be efficiently simulated on a\nquantum computer. The conclusion is two-fold: 1. TQFTs cannot be used to define\na model of computation stronger than the usual quantum model BQP. 2. TQFTs\nprovide a radically different way of looking at quantum computation. The rich\nmathematical structure of TQFTs might suggest a new quantum algorithm.",
"arxiv_id": "quant-ph/0001071",
"authors": [
"Michael H. Freedman",
"Alexei Kitaev",
"Zhenghan Wang"
],
"categories": [
"quant-ph",
"math.GT"
],
"doi": "10.1007/s002200200635",
"journal_ref": "Commun.Math.Phys. 227 (2002) 587-603",
"title": "Simulation of topological field theories by quantum computers",
"url": "https://arxiv.org/abs/quant-ph/0001071"
},
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