Implementation of a Clifford simulator in the quantum_info module

[renatomello]

Following an in-person discussion with @scarrazza, I will list here two enhancements that we need to implement as soon as possible:

• Clifford simulator following Aaronson and Gottesman (2004)
• Implementation of conversion of Clifford objects from tableaus to circuits in the normal form following Section 2.2. of Bravyi and Maslov (2020). The normal form is already implemented in quantum_info.random_clifford. We are missing the canonical form from Aaronson & Gottesman + conversion between the two representations.

[BrunoLiegiBastonLiegi]

Also this https://quantum-journal.org/papers/q-2021-07-06-497/ was suggested to me by @AlejandroSopena and might be relevant.

[alecandido]

Also this quantum-journal.org/papers/q-2021-07-06-497 was suggested to me by @AlejandroSopena and might be relevant.

I just found this again while inspecting https://github.com/quantumlib.

I'd say that integrating Stim would be more effective than rewriting from scratch.

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Furthermore, I found this other simulator you might already be aware of:

Implementation: https://github.com/asciineuron/bgls
Based-on paper: https://arxiv.org/abs/2112.08499

I wonder if you know whether there is any real advantage in having it, and if it's worth a separate issue.