W375 Westgate Building
11:00am
Title: Gradient Flows in Quantum Optimization
Abstract: First-order methods are the workhorse of modern machine learning, but they are notoriously inefficient in non-convex landscapes, frequently becoming trapped by local minima and saddle points. These classical limitations make them a prime target for quantum acceleration. In this talk, I will first establish a fundamental connection between gradient flows (i.e., the continuous-time limit of gradient descent) and the evolution of a continuous-variable quantum system under a corresponding Hamiltonian. This mapping yields a new class of quantum algorithms that not only inherit the efficiency of gradient descent but also leverage quantum tunneling to escape saddle points and local minima. I will present results demonstrating this quantum advantage, including provable speedups and superior empirical performance in finding global solutions. Finally, I will briefly survey some recent advances in generalizing this quantum dynamical approach to higher-order optimization methods.
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