[ HIGH PRIORITY ] Add tutorial on error mitigation with Qiskit Runtime Sampler

[kevinsung]

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Describe the new content you are requesting.

Split off from https://github.com/Qiskit/documentation/issues/1168

Relevant comment: https://github.com/Qiskit/documentation/issues/1168#issuecomment-2087262747

This tutorial is based on a summit demo and was refactored by Ritajit on Nate's team, please work with him on this issue.

• [ ] move source file into this repo
• [ ] review and refactor if needed. Address any feedback from product review in QTE repo

If this new content request is accepted, do you want to write the content?

I will write a draft of the proposed content

[kevinsung]

The Sampler primitive only exposes two error suppression options, dynamical decoupling and pauli twirling, arguably neither of which counts as "error mitigation." So the centerpiece of this tutorial, in my opinion, is the demonstration of how to manually perform readout error mitigation using mthree (related: https://github.com/Qiskit/documentation/issues/843).

However, mthree has yet to move from the old backend.run interface to the new Sampler interface, though there is an open issue for it. The existing source notebook works around this by manually constructing and running calibration circuits in a simplified but suboptimal procedure (it only uses two calibration circuits), and even with this simplified procedure, the code is too complex to be suitable for a tutorial.

So in my opinion, further work on this tutorial is blocked by mthree moving to the Sampler interface, which again is tracked by this issue: https://github.com/Qiskit-Extensions/mthree/issues/211