I'm currently learning about observable learning in quantum machine learning. I understand that the goal is often to predict the expectation value of a given observable (like a Pauli operator or a more general Hermitian matrix) with respect to some quantum state. See this reference for example: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.010602.
However, I'm a bit confused about what is actually being learned during training. Are we:
Trying to reconstruct an unknown quantum state by adjusting a parameterized quantum circuit (PQC) so that it approximates the state?
Or are we just learning a function that maps classical inputs to expectation values without reconstructing the full quantum state?
Are we optimizing over the parameters of a quantum circuit (like a variational ansatz), or is it something else?
Also, in practice, what does the loss function look like in this setting? Is it just the mean squared error between predicted and target expectation values?
Any explanation or even a simple example would help me a lot. I'm a PhD student new to quantum computing and programming, so beginner-friendly answers are appreciated!
