时间：4月20日（周一）上午10：00

地点：勤园20-518

报告简介：

A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\text{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $\mathcal{O}(k)$ copies of the state $\rho$, and we rigorously establish this lower bound under sample access to $\rho$. Surprisingly, this limitation can be overcome when one has purified access via a unitary that prepares a purification of $\rho$, a scenario naturally arising in quantum simulation and computation. In this setting, we find a different lower bound of $\Theta(\sqrt{k})$, and present a quantum algorithm that achieves this bound, demonstrating a quadratic advantage over sample-based methods. The key technical innovation lies in a designed quantum algorithm and optimal polynomial approximation theory---specifically, Chebyshev polynomial approximations tailored to the boundary behavior of power functions. Our results unveil a fundamental distinction between sample and purified access to quantum states, with broad implications for estimating quantum entropies and quantum Fisher information, realizing quantum virtual distillation and cooling, and evaluating other multiple nonlinear quantum observables with classical shadows.

报告人简介：

袁骁，博士，现任北京大学前沿计算研究中心助理教授，博士生导师，北京大学博雅青年学者，于2020年11月正式加入中心。他于2012年和2016年分别在北京大学和清华大学获学士、博士学位，之后于2017年、2017-2019年、2019-2020年分别在中国科学技术大学、牛津大学、斯坦福大学进行博士后研究。研究兴趣包括量子计算、量子信息、量子资源理论等。截至2024年1月，袁骁博士在物理领域顶级国际会议及期刊发表论文87篇 (including 1 in Review of Modern Physics, 15 in Physical Review Letters, 2 in Physical Review X, 4 in Nature, 1 in Nature Communication, 1 in Nature Review Physics, 7 in NPJ Quantum Information, 5 in Quantum, 2 in Chemical Science, 1 in Optica, 1 in IEEE Transactions on Information Theory, 1 in Science Bulletin, 1 in National Science Review)。加入中心后，袁骁博士创立量子模拟和量子信息实验室，该实验室的研究方向包括量子模拟算法设计、量子机器学习、量子基础理论等。