generate_cutting_experiments returns coefficients, not weights

[garrison]

I noticed that generate_cutting_experiments really returns coefficients, not weights. While weights (e.g., as returned by generate_qpd_weights) are all positive and can be rescaled arbitrarily, coefficients can be either positive or negative and cannot be rescaled arbitrarily. (Actually, the difference between weights and coefficients deserves some explanation, see #411.)

The misleading jump from "coefficients" to weights is in the following snippet:

https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/blob/f33317fde7de9f2c6a5c8916ff301a5388e3eedb/circuit_knitting/cutting/cutting_experiments.py#L144-L145

Interestingly, this was already labeled coefficients at the call site in cutting_experiments.py.

https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/blob/f33317fde7de9f2c6a5c8916ff301a5388e3eedb/circuit_knitting/cutting/cutting_experiments.py#L144-L145

[caleb-johnson]

Thanks, as I was rewriting some of this, I noticed that the coefficients returned from decompose are the actual scalars used during reconstruction (they're not manipulated again before scaling the sub-expvals by them). I have never really made a distinction between a weight and a scalar, but your explanation about being able to arbitrarily scale the values makes sense to me :)

[caleb-johnson]

Thanks!