Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Freedman, M.H. Quantum Computation and the Localization of Modular Functors . Found. Comput. Math. 1, 183–204 (2001). https://doi.org/10.1007/s102080010006
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s102080010006