Title: Mechanisms for Quantum Advantage in Global Optimization of Nonconvex Functions Speaker:  Shouvanik Chakrabarti (JPMorganChase) Date & Time:  October 20, 2025, 2:30pm Where to Attend:  ATL 3100A (VIRTUAL ONLY) Via Zoom: https://umd.zoom.us/j/94443622917?pwd=VqDYvKLHfBVEb9rnYP3C8XobjCbq6K.1 Password: nonconvex
We present new theoretical mechanisms for quantum speedup in the global optimization of nonconvex functions, based on a rigorous correspondence between the spectral properties of Schrödinger operators and the mixing times of classical Langevin diffusion. This correspondence motivates a mechanism for separation between quantum and classical algorithms on functions with a unique global minimum.We formalize these ideas by proving that a real-space adiabatic quantum algorithm (RsAA) achieves provably efficient, polynomial-time optimization for broad families of nonconvex functions. For block-separable functions, RsAA maintains polynomial runtime, whereas known off-the-shelf algorithms require exponential time and structure-aware algorithms can exhibit arbitrarily large polynomial runtimes. These results leverage novel non-asymptotic versions of semiclassical spectral analysis. Additionally, we use recent advances in intrinsic hypercontractivity to demonstrate polynomial runtimes for RsAA on appropriately perturbed strongly convex functions that lack global structure, while classical algorithms remain exponentially bottlenecked.In notable contrast to prior works based on quantum tunneling, these separations do not depend on the geometry of barriers between local minima. These findings establish a rigorous theoretical foundation for quantum advantage in continuous optimization and open new research directions connecting quantum algorithms, stochastic processes, and semiclassical analysis.
*Please note that this talk is VIRTUAL ONLY, however, you are welcome to view the virtual talk in ATL 3100A.*
*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*