Graphical Reasoning in Symmetric Monoidal Categories
Duration: 46 mins 51 secs
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About this item
| Description: | http://www.talks.cam.ac.uk/talk/index/22081 |
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| Created: | 2010-06-09 10:42 |
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| Collection: | Computer Laboratory Wednesday Seminars |
| Publisher: | University of Cambridge |
| Copyright: | Computer Laboratory |
| Language: | eng (English) |
| Abstract: | 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. |
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