[CS] James Sud MS PresentationApr 17, 2025

[via cs]

This is an announcement of James Sud's MS Presentation
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Candidate: James Sud

Date: Thursday, April 17, 2025

Time:  3 pm CST

Remote Location: https://uchicago.zoom.us/my/jamessud?pwd=Q2hyWS9iOGJja0ZrQ3FOd0VaQ09PUT09

Location: JCL 298

Title: Average-case algorithms for quantum optimization problems

Abstract: We design two variational algorithms to optimize specific 2-local Hamiltonians defined on graphs. Our algorithms are inspired by the Quantum Approximate Optimization Algorithm. We develop formulae to analyze the energy achieved by these algorithms with high probability over random regular graphs in the infinite-size limit. The complexity of evaluating these formulae scales exponentially with the number of layers of the algorithms, so our numerical evaluation is limited to a small constant number of layers. We compare these algorithms to simple classical approaches and a state-of-the-art worst-case algorithm. We find that the symmetry inherent to these specific variational algorithms presents a major obstacle to successfully optimizing the Quantum MaxCut (QMC) Hamiltonian on general graphs. Nonetheless, the algorithms outperform known methods to optimize the EPR Hamiltonian on random regular graphs, and the QMC Hamiltonian when the graphs are also bipartite. As a special case, we show that with just five layers of our algorithm, we can already prepare states within 1.62% error of the ground state energy for QMC on an infinite 1D ring, corresponding to the antiferromagnetic Heisenberg spin chain. 

Advisor: Fred Chong

Committee Members: Fred Chong, Bill Fefferman, Liang Jiang