From observations to complexity of quantum states via unsupervised learning

The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in nonequilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories. We use unsupervised learning with autoencoder neural networks to detect the local complexity of time-evolved states by determining the minimal number of parameters needed to reproduce local observations. The latter can be used as a probe of thermalization, to assign the local complexity of density matrices in open setups, and for the reconstruction of underlying Hamiltonian operators. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations.