Physics (Internal)

Simulated and Quantum Annealing Dynamics of the 2D Ising Model

This event is part of the Departmental Seminars.

Dissertation Committee: Anders Sandvik, Anatoli Polkovnikov, Shyam Erramilli, Alex Sushkov, and David Campbell

Abstract:

Developing methods of optimizing cost functions with complicated energy landscapes is an old and important idea that could be applied to many challenging computational problems. One of the simplest methods of accomplishing this optimization is through annealing. Annealing is a process where the dynamics of a physical system is simulated in a computer or in a real experiment to explore the energy landscape of the cost function. The hope being that if the fluctuations induced by the dynamics are tuned to 0 very slowly, the system will settle into the minimum of the cost function. In this talk we will explore the 2-D Ising model, comparing quantum annealing (QA) and a classical method of annealing through numerical simulations called simulated annealing (SA). Although the energy landscape is not rough or complicated, we find a distinct difference between QA and SA. We find two time scale associated with he relaxation of the system during SA. The faster time scale goes as L^2 while the slower time scale goes as L^3, L being the linear system size. We show that the slow time scale is associated with the formation of system spanning domain walls which pose difficulties for SA to anneal away. Contrast this with QA which shows only one time scale going as L^2, while at the same time showing signs of exploring the domain wall states during the annealing process. We will discuss these results in the context of the debate of whether quantum annealing is more efficient than classical methods for annealing. We will also discuss these results in the context of, what is claimed to be an actual quantum annealer, the D'wave quantum computer.