Hamiltonian Learning using Classical Shadows

Repo for experimenting with deep learning strategies to improve many body Hamiltonian Learning using Neural Differential Equations introduced by [T. Heightmann et al., 2024] using classical shadows. Our approach uses classical shadows to change the construction of the loss function used in [T. Heightmann et al., 2024]. We expect that our method using a new loss function has numerous advantages over using the old one. In particular, we expect that the limited coverage of Pauli bases can be overcome using classical shadows, which enable more accurate reconstruction of the probabilities $\langle b|\psi_{\theta}(t)\rangle |^2$ by aggregating data across different random measurement bases, while their randomized nature ensures uniform Hilbert space sampling and mitigates biases from restricted measurement bases.