刘正伟

刘锦鹏

2023年04月07日 09:30 至 10:30

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.

刘锦鹏，清华大学丘成桐数学科学中心助理教授。他曾于 2022 年至 2024 年在麻省理工和伯克利担任西蒙斯量子博士后研究员，于 2022 年获得马里兰大学博士学位。刘锦鹏的主要研究领域为量子模拟算法，量子科学计算，量子机器学习等。他开创性地发展了一系列量子算法用于求解微分方程、采样与优化问题，并解决了量子计算领域15年的公开猜想：提出首个多项式时间求解非线性微分方程的量子算法。他在PNAS、Nat. Commun.、PRL、CMP、JCP、Quantum 等期刊和 NeurIPS、QIP、TQC等会议发表论文多篇，并受到 Quanta、SIAM News、MATH+ 等科技媒体报道。他曾获得 ICCM 毕业论文奖（博士论文金奖）、NSF Robust Quantum Simulation Seed Grant （共同PI）、NSF QISE-NET Triplet Award、James C. Alexander Prize等荣誉。刘锦鹏现为量子信息领域顶刊Quantum的编委，是中国高校现有的3名编委之一。