Quantum supremacy and quantum phase transitions

Demonstrating the ability of existing quantum devices to perform certain computational tasks intractable to classical computers represents a cornerstone in quantum computing. Despite the growing number of proposed "quantum supreme'' tasks, it remains an important challenge to find their direct applications. In this work, we describe how the experiment proposed in Ref. [1] to demonstrate quantum supremacy in generic driven many-body systems can be extended to probe quantum phase transitions. We show how key quantum supremacy signatures, such as the distance between the output distribution and Porter Thomas distribution, can be used as order parameters. We apply this approach to a periodically driven disordered 1D Ising chain and show that we can capture the transition between the driven thermalized and many-body localized phases. The transition towards the Floquet prethermalized regime for high-frequency driving is also captured. Revisiting quantum phases of matter in the context of quantum supremacy draws additional links between complexity theory and many-body systems.

[1] J. Tangpanitanon, S. Thanasilp, M.A. Lemonde, N. Dangniam, D.G.Angelakis, arXiv:2002.11946 (2020)