The classical shadow estimation is a sample-efficient protocol for learning the properties of a quantum system through randomized measurements. For qubit systems, the efficiency of this approach is tied to the fact that the Clifford group forms a unitary 3-design. However, this property no longer holds for qudit systems, and it is substantially more difficult to understand the sample complexity of qudit shadow estimation. In this work, we show that qudit shadow estimation based on the Clifford group can achieve a similar performance as in qubit systems despite the crucial difference in the underlying group. Notably, the sample complexity of fidelity estimation is independent of the system size. Moreover, a single magic can significantly boost the efficiency and bridge the gap between qudit systems and qubit systems. These results may have profound implications for shadow estimation and quantum information processing based on qudits. Our work is based on a deep understanding of third moments of Clifford orbits, which is of independent interest.

报告人简介

朱黄俊，先后在浙江大学物理系、北京大学物理学院、和新加坡国立大学量子技术中心获学士、硕士、和博士学位。之后在加拿大圆周理论物理研究所和德国科隆大学理论物理研究所从事博士后研究。2018年1月至今在复旦大学物理学系任研究员。主要研究领域为量子信息基础理论，包括量子测量、量子层析、量子验证、纠缠理论、和盲量子计算等。以第一或通讯作者在国际知名期刊发表论文近50篇, 包括PRL 8篇，PRX Quantum 1篇，Nat. Commun. 1篇，和npj Quantum Inf. 3篇。

邀请人

王东升 副研究员