SMuK 2023 – scientific programme
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AKPIK: Arbeitskreis Physik, moderne Informationstechnologie und Künstliche Intelligenz
AKPIK 5: AI Topical Day – Neural Networks and Computational Complexity (joint session MP/AKPIK)
AKPIK 5.1: Talk
Wednesday, March 22, 2023, 11:00–11:30, ZEU/0250
A universal approach to state and operator complexities — •Souvik Banerjee1 and Mohsen Alishahiha2 — 1Julius-Maximilians-Universität Würzburg, Würzburg, Germany — 2IPM, Tehran, Iran
In this talk, I shall present a general framework in which both Krylov state and operator complexities can be put on the same footing. In our formalism, the Krylov complexity is defined in terms of the density matrix of the associated state which, for the operator complexity, lives on a doubled Hilbert space obtained through the channel-state map. This unified definition of complexity in terms of the density matrices enables us to extend the notion of Krylov complexity, to subregion or mixed state complexities and also naturally to the Krylov mutual complexity. We show that this framework also encompasses nicely, the holographic notions of complexity and explains the universal late-time growth of complexity, followed by a saturation.