Hello ,
I am Amit. I would like to discuss the implementation of modular
tensor categories for realization of Topological Quantum Computation. In
Topological Quantum Computation we use anyon braiding (which develops a
phase) to construct quantum gates which are nothing but unitary transforms.
The entire process of anyon braiding can be mathematically modeled by
representation of modular tensor categories. I have attached the article
through which I have gone through for understanding the implementation in
CAS. In addition to what is already present, most of the work is on
matrices. The 2 Vect spaces are isomorphic to whole numbers, 1 cells are
represented by matrices and 2 cells are represented by inner matrices (or 2
matrices) i.e., matrices inside matrices. Most of the implementation is by
using the properties of matrices and extending the present implementation
of matrices. The implementation then tested the Fibonacci model by
mentioning the fusion rules. I would like add this functionality to Sympy
and if possible carry it out as a part of GSoC 2014. According to my
understanding the implementation is mostly mathematical but the physical
extension is to TQC by testing the Fibonacci model. I request the community
to comment on this. Thanks.
File :
http://ora.ox.ac.uk/objects/uuid%3Ac9b6eaf8-29d4-4637-a576-5a35d3c957bb/datastreams/THESIS01
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