Topological Quantum Computation
Michael H. Freedman, Alexei Kitaev, Michael J. Larsen, and Zhenghan, Wang

TL;DR
This paper explores topological quantum computation, which uses anyonic systems modeled by modular functors, offering a potentially more robust approach to quantum error correction compared to traditional qubit models.
Contribution
It links topological quantum field theory with quantum computation, highlighting the advantages of anyonic systems for error-resistant quantum computing.
Findings
Anyons modeled by modular functors enable topological quantum computation.
Topological error correction scales exponentially with system size.
Potential for physically realizable, error-resistant quantum computers.
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 , where is a length scale, and is some positive constant. In contrast, the presumptive" qubit-model of quantum computation, which repairs errors combinatorically, requires a fantastically low initial error rate (about ) before computation can be stabilized.
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum Computing Algorithms and Architecture · Topological and Geometric Data Analysis
