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# Vadim N. Smelyanskiy: Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape

## October 11, 2019 @ 12:00 pm - 2:00 pm

Friday 11.10.2019, 12:15h in Kuščerjev seminar, Jadranska 19.

We will review the advances and challenges in the field of quantum combinatorial optimization and closely related problem of low-energy eigenstates and coherent dynamics in transverse field quantum spin glass models. We will discuss the role of collective spin tunneling that gives rise to bands of delocalized non-ergodic quantum states providing the coherent pathway for the population transfer (PT) algorithm: the quantum evolution under a constant transverse field that starts at a low-energy spin configuration and ends up in a superposition of spin configurations inside a narrow energy window. We study the transverse field induced quantum dynamics of the following spin model: zero energy of all spin configurations except for a small fraction of spin configuration that form a narrow band at large negative energy. We use the cavity method for heavy-tailed random matrices to obtain the statistical properties of the low-energy eigenstates in an explicit analytical form. In a broad interval of transverse fields, they are non-ergodic, albeit extended giving rise to a qualitatively new type of quantum dynamics. We argue that our approach can be applied to study PT protocol in other optimization problems with the potential quantum advantage over classical algorithms.

***** *Vadim N. Smelyanskiy, Google Quantum AI
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