New Chapter - Between the quibits and me

[Scinawa]

Write chapter on development, compilation, error correction, and optimization of quantum circuits on real hardware. Somehow, it is pretty daunting to understand all the process that occur (or will occur) from the moment we finished writing our algorithm in a high level language (such as a python library), and the moment when we execute our code on a hardware platform. Here we should give the high-level understanding of what is going on, so the practitioner in quantum algorithms can have an idea of all the layers of abstractions that are between the software and the hardware.

There should be a new chapter (more or less 10 pages), covering the following topics:

• Hardware that we can target right now
• Compilation of a circuit for a specific hardware ( Solovay–Kitaev and further improvements)
• Optimization of the circuit (ZX calcolus, rewriting rules, other optimization methods)
• Error correcting code (introduction, state of the art). The difference between error-correction and fault tolerance?
• Mapping circuit to a given topology (swap counts)