Summary

This PR depends on #14283

This adds the PauliLindbladMap class to quantum_info. This class stores very similar data to SparseObservable, but the list of operators is now stored within the QubitSparsePauliList introduced in #14283.

It also adds the "derived" properties:

• gamma - the overall gamma of the map.
• probabilities - the probability of application for each Pauli operator in the pseudo-probabilistic product representation.
• non_negative_rates - a vector of booleans evaluating rate >= 0 for each rate in rates.

The above are "derived" in the sense that they are functions of the rates. As a result they have been setup to be non-writable, and to be updated if rates is ever mutated.

Details and comments

The one thing I'm uncertain about is that there is a lot of overlap between the docs of PauliLindbladMap and QubitSparsePauliList in terms of the Pauli symbol/bit property. Currently the internally stored QubitSparsePauliList is not accessible from PauliLindbladMap - the properties/methods of PauliLindbladMap are set up so that it looks like all the information in QubitSparsePauliList (paulis, indices, boundaries) is directly stored by PauliLindbladMap. With this current interface, it doesn't seem to me make sense to reference back to QubitSparsePauliList if there is no explicit connection between the classes. I think I'm fine with this but am open to suggestions.