Zala Lenarčič (JSI): From observations to complexity of quantum states: an unsupervised learning approach

The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatments, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories. I will discuss how unsupervised learning can detect the local complexity of states. This approach can be used as a probe of scrambling and thermalization in chaotic quantum systems or to assign the local complexity of density matrices in open setups without knowing the corresponding Hamiltonian or Liouvillian. The analysis actually allows for the reconstruction of Hamiltonian operators or even noise-type that might be contaminating the measurements. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations. For example, it would be perfectly suited to detect the many-body localization transition or integrability effects from the experimental snapshots obtained with cold atoms. [1] M. Schmitt and Z. Lenarčič, arXiv:2102.11328