3D Quon Language

.Alex Wozniakowsi, Arthur Jaffe, and Zhengwei Liu

New Insights into Quantum Information

We introduced a 3-dimensional language into quantum information, using charged strings in three-manifolds.  For a 1-qudit transformation, we replace our 2-string model by a 4-string model. This allows us to use more powerful isotopy tools that extend the ideas in the 2-string model. In this language we can realize all Clifford gates as a single picture of a three-manifold with embedded charged strings. Consequently this model is universal for measurement-based quantum computation. Our model is linear, and we can realize all transformations as a linear sum of pictures. But we emphasize the use of single pictures and 3D isotopy. 

New Insights into Other Subjects

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Arthur Jaffe and Zhengwei Liu, A Mathematical Picture Language Program. PNAS

Zhengwei Liu, Quon Language: Surface Algebras and Fourier Duality. arXiv: 1707.03995

Jacob Biamonte, Charged String Tensor Networks. The Biamonte paper is a commentary on, “Quon 3D Language for Quantum Information.” arXiv: 1703.01302PNAS

Zhengwei Liu, Alex Wozniakowski, and Arthur Jaffe. Quon 3D Language for Quantum Information. arXiv: 1612.02630PNAS

6-j Symbol Duality