Seminar 13 – The Clifford project

Project

This week, we started working on the project with the goal of proving the following Theorem 1 of SIC-POVMs and the extended Clifford group (D. M. Appleby, 2005) for the special case where $d$ is an odd prime. In summary, the theorem states that the projective Clifford group on one $d$-dimensional qubit is isomorpic to the affine symplectic group over $\mathbb{Z}_d$:

\[\mathrm{C}(d) / \mathrm{I}(d) \simeq \mathrm{Sp}(2, \mathbb{Z}_d) \ltimes \mathbb{Z}_d.\]

Find the pre-digested proof a blueprint here at https://marozols.github.io/clifford-project/ Find the GitHub project with instructions on how to contribute at https://github.com/marozols/clifford-project

If you want to participate in the formalization, make sure you are on Zulip and have a GitHub account. Then share your GitHub username with Maris on Zulip so that he can give you push access to the project repository.
Afterwards, follow the instructions on the GitHub page.
Always feel free to ask for help!