Sparse observables with extended alphabets

[jakelishman]

Summary

This describes a new SparseObservable object that would be added to qiskit.quantum_info for use in the Estimator interface, to address two major problems:

• the Pauli alphabet of SparsePauliOp makes it impossible to efficiently represent all operators that can be efficiently measured by hardware.
• as device qubit counts scale up, the number of non-identity terms in observable terms does not necessarily do so, making the SparsePauliOp representation inefficient.

Scope

This design doc is just about what the new class will look like. A key component of that is making sure that it can be used in Estimator implementers, but the exact mechanisms of how the public Estimator interface evolves to accept this are out-of-scope of this document.

[blakejohnson]

Looks like a strong proposal.