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Graphical Reasoning in Symmetric Monoidal Categories

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If you have a question about this talk, please contact Mateja Jamnik.

Symmetric monoidal categories capture the basic structure of a variety of important domains, including quantum computations. An important feature is that they have a natural visual presentation that is similar to traditional circuit diagrams. Additional structure specific to a domain, such as quantum information, is sometimes captured as equations between diagrams. Informally, such equations may involve ‘ellipses’-notation (as in the “1 … n” notation used for a list of numbers from 1 to n). I will describe how such notation in graphs can be made amenable to computer-aided manipulation, why this is important, and the interesting structural properties that result. I will illustrate the graphical language applied to quantum computations and boolean circuits.

Finally, I will show how this can be used to perform a graphical version of symbolic proof and computation.

This talk is part of the Computer Laboratory Wednesday Seminars series.

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