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