Quantum supremacy and quantum phase transitionsQuantum supremacy and quantum phase transitions Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2022-12-072021enThis research was partially funded by the Polisimulator project co-financed by Greece and the EU Regional Development Fund.Demonstrating the ability of existing quantum platforms to perform certain computational tasks intractable to classical computers represents a cornerstone in quantum computing. Despite the growing number of such proposed “quantum supreme” tasks, it remains an important challenge to identify their direct applications. In this work, we describe how the approach proposed by Tangpanitanon et al. [arXiv:2002.11946] for demonstrating quantum supremacy in generic driven analog many-body systems, such as those found in cold atom and ion setups, can be extended to explore dynamical quantum phase transitions. We show how key quantum supremacy signatures, such as the divergence between the output distribution and the Porter Thomas distribution, can be used as effective order parameters. We apply this approach to a periodically driven disordered one-dimensional Ising model and show that we can accurately capture the transition between the driven thermalized and many-body localized phases. This approach also captures the transition towards the Floquet prethermalized regime for high-frequency driving. Revisiting quantum phases of matter under the light of the recent discussions about quantum supremacy draws a link between complexity theory and analog many-body systems.http://creativecommons.org/licenses/by/4.0/Physical review B10316 Thanasilp Supanut Tangpanitanon Jirawat Lemonde Marc-Antoine Dangniam Ninnat Angelakis Dimitrios Αγγελακης Δημητριος American Physical Society Dynamical phase transitions Eigenstate thermalization Many-body localization Order parameters Phase diagrams Quantum phase transitions Quantum simulation Disordered systems Floquet systems