Categorical Tensor Network States
Stephen R.Clark Jacob D. Biamonte and Dieter Jaksch
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Abstract
We examine the use of the mathematics of category theory in the description
of quantum states by tensor networks.
This approach enables the development of
a categorical framework allowing a solution to the quantum decomposition
problem. Specifically, given an n-body quantum state ψ, we present
a general method to factor ψ into a
tensor network. Moreover, this
decomposition of ψ uses building blocks defined mathematically in
terms of
purely diagrammatic laws. We use the solution to expose a previously
unknown and large class of quantum states which
we prove can be sampled
efficiently and exactly. This general framework of categorical tensor network
states,
where a combination of generic and algebraically defined tensors
appear, enhances the theory of tensor network states.
Blogs about this paper:
(i) http://golem.ph.utexas.edu/category/2010/09/bimonoids_from_biproducts.html
(ii) http://johncarlosbaez.wordpress.com/2010/09/29/jacob-biamonte-on-tensor-networks/
Talks about this paper:
(i) http://new.iqc.ca/news-events/calendar/generated/jacob-biamonte-2010-12-2
(IQC, Institute for Quantum Computing
University of Waterloo, Canada)
Link to arXiv version:
* http://arxiv.org/abs/1012.0531
Details
| Institution |
OUCL |
| Journal |
arXiv:1012.0531v1 [quant−ph] |
| Keywords |
Tensor Networks‚ Simulation‚ MPS‚ CTNS‚ PEPS‚ MERA‚ Category Theory‚ Quantum Mechanics and Quantum Theory |
| Month |
Sep |
| Number |
RR−10−14 |
| Pages |
31 |
| Year |
2010 |
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