10.1 The Variational Approach
Let us start with recollecting the details of training discriminative (QNN) and generative (QCBM) models. In both cases, our task was to find an optimal configuration of PQC parameters (e.g., rotation angles of adjustable one-qubit gates) such that the resulting quantum state had the desired properties: we could either sample from the encoded probability distribution (generative model) or obtain a class label for the given sample (discriminative model). The process of finding an optimal configuration of PQC parameters is called learning when we are dealing with QML use cases. This learning can be done either in a differentiable or in a non-differentiable way, but it always consists of the minimisation of some cost function through varying the adjustable circuit parameters.
What if the cost function we want to minimise is encoded in the problem Hamiltonian and the task is formulated as finding its ground state? In Chapter 3, we saw how this problem can...
