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SYML: Symposium Machine Learning in Atomic and Molecular Physics

SYML 1: Machine Learning in Atomic and Molecular Physics

SYML 1.4: Invited Talk

Tuesday, March 7, 2023, 12:30–13:00, E415

Efficient quantum state tomography with convolutional neural networks — •Moritz Reh¹, Tobias Schmale², and Martin Gärttner^{1, 3, 4} — ¹Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany — ²Institut für Theoretische Physik, Universität Hannover, Welfengarten 1, 30167 Hannover — ³Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany — ⁴Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

Capturing the properties of quantum many-body systems poses a major challenge from a theoretical standpoint, as both the task of numerical simulation as well as the characterization of an experiment from sparse data are suffering from the curse of dimensionality. Variational approaches based on neural networks have therefore become popular, mitigating the curse of dimensionality by searching for a solution in an artificially reduced space. We will motivate and introduce a particular class of such a scheme that allows to describe mixed states in spin systems, before showing its application to quantum state tomography (QST). We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomially in system size. This compressed representation allows us to reconstruct states with high classical fidelities outperforming standard methods such as maximum likelihood estimation of the full density matrix.