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Tech. Note: On the Weyl chamber of canonical non-local 2-qubit gates

weyl

Tech. Note 012v1

PDF:
http://threeplusone.com/weyl

Source code:
https://github.com/gecrooks/on_weyl

The Weyl chamber of canonical non-local 2-qubit gates. Papercraft meets quantum computing. Print, cut, fold, and paste. (Should look like Fig. 4 of quant-ph/0209120)

A 2-qubit gate has 15 free parameters. But you can apply local 1-qubit gates before and after, which leaves a 15-4×3=3-parameter space of non-local gates. Once you remove a bunch of symmetries, you’re left with a tetrahedral chamber in which all your favorite 2-qubit gates live.