Foundations of Computational Mathematics

, Volume 1, Issue 2, pp 183–204

Quantum Computation and the Localization of Modular Functors


DOI: 10.1007/s102080010006

Cite this article as:
Freedman, M.H. Found. Comput. Math. (2001) 1: 183. doi:10.1007/s102080010006


The mathematical problem of localizing modular functors to neighborhoods of points is shown to be closely related to the physical problem of engineering a local Hamiltonian for a computationally universal quantum medium. For genus =0 surfaces, such a local Hamiltonian is mathematically defined. Braiding defects of this medium implements a representation associated to the Jones polynomial and this representation is known to be universal for quantum computation.

AMS Classification

Primary 57R56 Secondary 68Q05, 81Q70, 82B10, 94B99, 20F36 

Copyright information

© Society for the Foundation of Computational Mathematics 2000

Authors and Affiliations

  1. 1.Microsoft ResearchOne Microsoft WayRedmondUSA

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