报告题目：From quantum search to query-based  eigensolver and spectral clustering

报 告 人：王晓霆 教授（电子科技大学）

报告时间：2022年7月17日(周日)8:00--9:00

报告方式：数学学院201室

报告摘要：Grover's search algorithm is fundamental in quantum computing and serves as a critical building block for many other algorithms, including query-based eigensolver and spectral clustering. Clustering is one of the most crucial problems in unsupervised learning, and the well-known k-means algorithm can be implemented on a quantum computer with a significant speedup. However, for the clustering problems that cannot be solved using the k-means algorithm, a powerful method called spectral clustering is used. In this talk, we propose a circuit design to implement spectral clustering on a quantum processor with substantial speedup by initializing the processor into a maximally entangled state and encoding the data information into an efficiently simulatable Hamiltonian. Compared to the established quantum kmeans algorithms, this method does not require a quantum random access memory or a quantum adiabatic process. It relies on an appropriate embedding of quantum phase estimation into Grover's search to gain the quantum speedup. Simulations demonstrate that such method effectively solves clustering problems and provides an important supplement to quantum k-means algorithm.

个人简介：电子科技大学基础与前沿研究院教授、博士生导师。本科毕业于武汉大学，硕士博士毕业于剑桥大学。先后在美国麻省大学波士顿分校，麻省理工学院，路易斯安那州立大学开展科研工作。研究方向包括量子计算、量子机器学习、量子优化、量子控制、量子精密测量等，其学术成果发表在 Physical Review Letters, npj Quantum Information, IEEE TAC 等刊物。代表性工作包括：1. Phys. Rev. Lett. 117, 170501 (2016)；2. Phys. Rev. Lett. 116, 090404 (2016)；3. Phys. Rev. Lett. 114, 170501 (2015)；4. Phys. Rev. Lett. 110, 157207 (2013)；5. Phys. Rev. Lett. 107, 177204 (2011).