From observations to complexity of quantum states via unsupervised learning

Abstract

The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium 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.

6+6 pages, 3+6 figures

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Cited by in corpus (10)

• Measurement-induced criticality as a data-structure transition
• Entanglement Barriers in Dual-Unitary Circuits
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Thermometry of one-dimensional Bose gases with neural networks
• Data-driven discovery of statistically relevant information in quantum simulators
• Iterative construction of conserved quantities in dissipative nearly integrable systems
• Reconstructing effective Hamiltonians from nonequilibrium (pre-)thermal steady states
• Quantum memory at an eigenstate phase transition in a weakly chaotic model
• Generalized Gibbs ensembles in weakly interacting dissipative systems and digital quantum computers
• Learning the non-Markovian features of subsystem dynamics