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Progress toward favorable landscapes in quantum combinatorial optimization
*This event is in-person and open only to Princeton University ID holders
Progress toward favorable landscapes in quantum combinatorial optimization
The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. In this talk, I explore how these quantum and classical components interrelate. In particular, I focus on algorithms for solving the combinatorial optimization problem MaxCut and study how the structure of the classical optimization landscape relates to the quantum circuit used to evaluate the MaxCut objective function. In order to analytically characterize the impact of quantum features on the landscape critical point structure, I consider a family of quantum circuit ansätze composed of mutually commuting elements. I identify multiqubit operations as a key resource and show that overparameterization allows for obtaining favorable landscapes. Namely, I prove that an ansatz from this family containing exponentially many variational parameters yields a landscape free of local optima for generic graphs. However, I further show that these ansätze do not offer superpolynomial advantages over purely classical MaxCut algorithms. I then present a series of numerical experiments illustrating that non-commutativity and entanglement are important features for improving algorithm performance.
Christian is currently a lecturer and an associate research scholar in the Department of Chemistry at Princeton University. Previously, he completed his Ph.D. in applied mathematics at Aberystwyth University (UK) in 2016, where he focused on the control of open and noisy quantum systems. Christian will join Arizona State University as an assistant professor in the School of Electrical, Computer and Energy Engineering in January 2022. Christian’s research centers on using tools from control theory to advance quantum information science. His work targets applications such as the design of robust and efficient controls for quantum computing, and the development of quantum algorithms for optimization and machine learning tasks.