Symmetries have proven useful in machine learning models, improving generalisation and overall performance.

We propose a versatile framework that combines DEQ with off-the-shelf machine learning models for predicting Hamiltonians.

Our algorithm incorporates constraints into the Riemannian version of Hamiltonian Monte Carlo and maintains sparsity.

See Appendix Aforanoteontrain/testsplitfor Task 3. loss Testloss Energy Baseline HNNBaseline HNNBaseline HNN mass-spring170 20.38 .1 pendulum 42 10 25 5 pendulum 390 7 14 5 (6.3e4 3e4 39 5 pendulum.3

Despite these advancements, QAOA's practical efficacy is challenged by the quantum coherence limits of modern quantum devices, as there is a ceiling on the allowable maximum circuit depth