Zhengwei Liu

Jinpeng Liu

Friday, April 7, 2023 9:30 AM - 10:30 AM

JCY-1

Tencent 494 8360 9451 (2023)

Nonlinear dynamics play a prominent role in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear equations have been severely limited due to the linearity of quantum mechanics, we gave the first efficient quantum algorithm for nonlinear differential equations with sufficiently strong dissipation. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in the evolution time. We also established a lower bound showing that nonlinear differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics.   Furthermore, we designed end-to-end quantum machine learning algorithms, combining efficient quantum (stochastic) gradient descent with sparse state preparation and sparse state tomography. We benchmarked instances of training sparse ResNet up to 103 million parameters, and identify the dissipative and sparse regime at the early phase of fine-tuning could receive quantum enhancement. Our work showed that fault-tolerant quantum algorithms could potentially contribute to the scalability and sustainability of most state-of-the-art, large-scale machine learning models.   References: [1] Liu et al. Efficient quantum algorithm for dissipative nonlinear differential equations, Proceedings of the National Academy of Science 118, 35 (2021), arXiv:2011.03185. [2] Liu et al. Towards provably efficient quantum algorithms for large-scale machine learning models, arXiv:2303.03428.

Jin-Peng Liu is an assistant professor at YMSC, Tsinghua University. He was a Simons quantum postdoctoral fellow at MIT and Berkeley from 2022 to 2024. He received his Ph.D. from the University of Maryland in 2022. His research focuses on Quantum for Science and AI+QS. He has published papers in PNAS, Nat. Commun., PRL, CMP, JCP, Quantum, and NeurIPS, QIP, TQC. His research has been reported by Quanta, SIAM News, and MATH+. He has won the ICCM Best Thesis Award (Gold Prize), NSF Robust Quantum Simulation Seed Grant (CO-PI), NSF QISE-NET Triplet Award, and James C. Alexander Prize. He is serving as an editor of Quantum (JCR Q1, IF 6.4).