Learning Minimal Representations of Fermionic Ground States
This work addresses the challenge of efficiently modeling fermionic systems in quantum physics, offering a novel approach that could impact computational methods in the field.
The paper tackles the problem of representing quantum many-body ground states by introducing an unsupervised machine-learning framework that discovers optimally compressed representations, achieving a sharp reconstruction quality threshold at L-1 latent dimensions for Fermi-Hubbard models and enabling energy minimization directly within the latent space while circumventing the N-representability problem.
We introduce an unsupervised machine-learning framework that discovers optimally compressed representations of quantum many-body ground states. Using an autoencoder neural network architecture on data from $L$-site Fermi-Hubbard models, we identify minimal latent spaces with a sharp reconstruction quality threshold at $L-1$ latent dimensions, matching the system's intrinsic degrees of freedom. We demonstrate the use of the trained decoder as a differentiable variational ansatz to minimize energy directly within the latent space. Crucially, this approach circumvents the $N$-representability problem, as the learned manifold implicitly restricts the optimization to physically valid quantum states.