I understand there are some efficient encoding schemes for variational algorithms, that attempt to approximate the variational state using fewer qubits. I'm thinking of 2 papers in particular, which are very closely related:
https://arxiv.org/abs/2007.01774: SEction 3 "Minimal Encoding"
https://arxiv.org/pdf/2306.08507: Section V " SYSTEMATIC ENCODING OF BINARY VARIABLES"
The main idea is to approximate the parameterized quantum state using fewer qubits. To me, this seems like it's only possible given a circuit-based quantum computing model (e.g. IBM's quantum computers). Does the idea still apply to annealers such as those provided by Fujitsu and DWave?