So far I have read a little bit about zx-calculus & y-calculus.

From Reversible Computation:

The zx-calculus is a graphical language for describing quantum systems.

The zx-calculus is an equational theory, based on rewriting the diagrams which comprise its syntax. Re-writing can be automated by means of the quantomatic software.

This method seems very interesting, however I am not able to find much introductory information on the subject. Any insight into the subject or additional resources would be greatly appreciated.

Current Resources:

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    $\begingroup$ By introductory information, do you mean like about string diagrams for monoidal categories in general? $\endgroup$ – AHusain Jul 16 '18 at 0:48
  • $\begingroup$ @AHusain Upon further investigation, it seems so (added link) $\endgroup$ – meowzz Jul 16 '18 at 1:15

The best possible reference at the moment is

It is written by one of the two inventors of the ZX calculus (Bob Coecke), and one of the people who has contributed the most to the development of Quantomatic (Aleks Kissinger), and so would be the definitive introductory reference.


You already put Selinger's survey, so here are a couple more links

Baez and Stay. You could see other Baez blog posts as well.

Qiaochu Yuan's blog. See later in that series as well.


Baez and Stay is a survey article. It covers monoidal, braided, symmetric and dagger categories. For the example related to quantum computation focus on either Hilb or cobordism. The appropriate string diagrams for these are included along with the sections for those types of categories. It points the connections between logic and type theory as well, but you don't need those sections. However it would be helpful.

Qiaochu's blog post is more introductory and brief. It focuses solely on the vector space example as to avoid prerequisites besides linear algebra. The later posts in that series cover other adjectives to add on such as braided, symmetric or dagger.

  • $\begingroup$ Any resources on braided monoidal categories? $\endgroup$ – meowzz Jul 16 '18 at 2:08
  • $\begingroup$ Please expand more on why these are good resources; see our resource request policy. Thanks! $\endgroup$ – heather Jul 16 '18 at 18:16

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