University of Minnesota
School of Physics & Astronomy

Physics and Astronomy Calendar

Wednesday, September 11th 2019
1:25 pm:
Speaker: Vadim Smelyanskiy, Google, Los Angeles
Subject: Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape

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. For large transverse
fields the typical runtime of PT algorithm scales with n and  as that of the Grover’s quantum
search, except for the small correction to the exponent . The model we consider is non-
integrable. As a result, our PT protocol does not require any fine-tuning of and may be
initialized in a computational basis state. We argue that our approach can be applied to study PT
protocol in other optimization problems with the potential quantum advantage over classical
algorithms.

Faculty Host: Alex Kamenev

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