Theory Seminar: Hamiltonian-oriented Quantum Algorithm Design and Programming

Prof. Xiaodi Wu
University of Maryland
Theory Seminar, at the Lecture Hall
Wednesday, March 04, 11:30 CET

We propose a Hamiltonian-oriented paradigm for end-to-end quantum application design, motivated by the observation that quantum Hamiltonian evolution provides a native abstraction for both low-level hardware control and high-level quantum algorithms. By placing Hamiltonian evolution at the center of the design process, this paradigm enables more efficient implementations of existing quantumalgorithms and also inspires new ones—particularly in optimization and scientific computing—whose structure may be difficult to recognize within the traditional circuit model.

In particular, we introduce Quantum Hamiltonian Descent (QHD), a quantum optimization framework derived from the path integral formulation of classical dynamical systems. We establish strong theoretical guarantees and empirical evidence for its effectiveness, showing exponential quantum–classical separation for certain oracular continuous optimization problems and super-polynomial advantages over state-of-the-art classical solvers on a nonconvex degree-4 polynomial optimization task. We further enable its practical deployment through a novel Hamiltonian embedding technique and experimentally demonstrate QHD on an analog quantum Ising simulator with over 5000 spins, solving nonconvex box-constrained quadratic programming problems up to 75 dimensions. To support broader adoption, we have released QHDOPT, a user-friendly software package built on the QHD framework.