Randomized benchmarking and gate-set shadow estimation

[scarrazza]

Roadmap from @ingoroth:

• [x] port existing qiborb functionality to qibocal to restore standard (single qubit Clifford) RB implementation https://github.com/qiboteam/qcvv/pull/92
• [x] Make scheme executable on quantum hardware
• [ ] Implement error bars
  • [ ] for standard RB
  • [ ] for filtered RB
• [x] implement ‘filtered' randomized benchmarking for non-self-inverting sequences (single qubit Clifford group)
• [ ] implement (higher-order) simultaneous RB via filtering for all irreps (novel publishable scheme)
  • [ ] (graphical plot/report for (higher-order) simultaneous RB)
• [ ] random Gate classes for other groups {1, X}, ... , Heisenberg-Weyl, Dihedral
• [ ] non-uniform generator RB (random gate classes that draw from generators)
  • [ ] (spectral gap computing tools for determining minimal required length for non-uniform RB)
• [ ] multi-qubit Clifford RB
• [ ] universal random-circuit RB (XEB and so on)
• [ ] cross-talk tomography (novel publishable scheme)
  • [ ] (single exponential decay fitting for hetero-skedastic data + error bars (e.g. weighted linear least-squares) + statistical tests)

[wilkensJ]

First rb data from 5 qubit chip, run on qubit 2.

[andrea-pasquale]

I believe that this issue is outdated given that there is #411. Shall we close it?

[wilkensJ]

Yes thank you @andrea-pasquale.