Learning Minimal Representations of Fermionic Ground States

TL;DR

This paper presents an unsupervised machine learning approach using autoencoders to find minimal, physically valid representations of fermionic ground states, enabling efficient energy minimization without the N-representability problem.

Contribution

It introduces a novel autoencoder-based framework that discovers minimal quantum state representations and uses the decoder as a variational ansatz, bypassing traditional constraints.

Findings

Identifies minimal latent spaces with L-1 dimensions for L-site models

Uses the decoder as a differentiable variational ansatz for energy minimization

Circumvents the N-representability problem through learned quantum manifolds

Abstract

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.