LRE Functions: Noise Scaling

[purva-thakre]

Use this issue to add the functionality for creating noise-scaled circuits using LRE. As discussed in the RFC, we are chooisng to create a separate module mitiq/lre instead of relying on mitiq/zne.

mitiq/zne/scaling/layer_scaling.py requires a list of which layers a user wants to fold. With the LRE method, each layer gets folded differently depending on the chosen int value known as the fold_multiplier in the Jupyter notebook and minimum_noise_scaling_gap in the LRE paper.

If a user wants to fold only a specific list of layers, they won't be able to use multi-variate Richardson extrapolation.

1. A function to find the number of layers in the input circuit without terminal measurements.
2. If a user wants to chunk a large input circuit into smaller chunks, a function to create the chunked layers.
3. A function to generate the scale factor vectors required by the specific folding pattern
4. A function to generate multiple noise-scaled but logically equivalent circuits.