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TT: Fachverband Tiefe Temperaturen

TT 8: Focus Session: Quantum Interactive Dynamics I (joint session DY/TT)

TT 8.9: Vortrag

Montag, 18. März 2024, 12:15–12:30, A 151

Efficient Learning of Matrix Product States for Approximation of Purities in Quantum Many-Body Systems — •Dmytro Kolisnyk, Raimel Medina, and Maksym Serbyn — Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria

The defining feature of quantum many-body systems is an exponential scaling of the Hilbert space with the number of degrees of freedom. This exponential complexity naïvely renders the complete characterization of state, for instance via the complete set of bipartite Renyi entropies, a challenging task. Recently, the compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as the entanglement feature (EF), was proposed. Matrix product state (MPS) encoding of such EF was obtained for Haar random states, however, the general applicability and practical usage of such encoding remained unclear. In this work, we demonstrate that EF can be efficiently learned using only polynomial amount of samples in the number of degrees of freedom through the so-called TTcross algorithm, assuming it is expressible as a finite bond dimension MPS. We benchmark this learning process on Haar and random MPS states, utilizing analytic insights. Additionally, we devise novel applications for the learned EF, such as quantifying the distance between different entanglement patterns and finding the optimal one-dimensional ordering of physical indices in a given state, highlighting the potential utility of proposed learning method in characterizing quantum many-body systems.

Keywords: Entanglement feature; Matrix product state; Entanglement entropy