[WIP] First notebook in the QEC Tutorial

[abidart]

This PR has the first version of part 1 of a 3-part QEC tutorial I am working on. It uses Bloqade's squin dialect to construct circuits. This 3-part tutorial on error correction is inspired by some of the techniques and codes used in recent work from QuEra and collaborators, and Quantinuum.

Could this content be relevant to this repository? Otherwise I can keep it on a separate repository.

The goal of this specific tutorial is for the reader to explore the basics of error correction and logical operations. The tasks revolve around comparing the performance of:

• a 2-qubit circuit with a noisy CX gate vs.
• a 14-qubit circuit with two instances of the [[7, 1, 3]] Steane code and a noisy transversal CX.

Two visualizations that compare the performance of the final circuits across multiple runs and across (slightly) different noise models are presented at the end.

More specifically, the ideas for this tutorial came from:

• Bluvstein, Dolev, et al. "Logical quantum processor based on reconfigurable atom arrays." Nature 626.7997 (2024): 58-65.
• Sales Rodriguez, Pedro, et al. "Experimental demonstration of logical magic state distillation." Nature 645.8081 (2025): 620-625.
• Ryan-Anderson, C., et al. "Implementing fault-tolerant entangling gates on the five-qubit code and the color code." arXiv preprint arXiv:2208.01863 (2022).