1. 量子导引 （Quantum steering）的刻画、度量和探测

      量子导引描述了关联的微观系统中一个子系统对另一个系统的操控能力。我们主要利用量子导引椭球这种几何工具来研究量子导引这种现象，探索量子导引椭球与量子纠缠和 Bell 非定域性等量子关联之间的联系与区别，并且设计具有鲁棒性的物理实验可实现的方案来重构量子导引椭球和发掘其与其它量子关联的联系。

2. 研究多体量子系统中量子资源的分布现象：单配关系（Monogamy and trade-offs） 

      量子纠缠等量子关联在多体系统中不能够被随意自由分配，这一现象称为单配关系。我们主要利用适当的数学工具来量化量子关联存在的单配关系，并且研究在不同的方案下所需要的量子资源是否存在单配关系这一现象。

3. 探究 NISQ 量子算法和机器学习的结合

谷歌学术主页：https://scholar.google.com/citations?user=QB0VeqkAAAAJ&hl=en

学术文章 arXiv 合集：Shuming Cheng's articles on arXiv

1. Yuan-Yuan Zhao, Chao Zhang, Shuming Cheng*, Xinhui Li, Yu Guo, Bi-Heng Liu, Huan-Yu Ku, Shin-Liang Chen, Qiaoyan Wen, Yun-Feng Huang, Guo-Yong Xiang, Chuan-Feng Li, and Guang-Can Guo. Device-independent verification of quantum steering, arXiv: 1909.13432.

2. Yu Guo, Shuming Cheng*, Xiaomin Hu, Bi-Heng Liu, En-Ming Huang, Yun-Feng Huang, Chuan-Feng Li,  Guang-Can Guo, Eric G Cavalcanti. Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits. Phys. Rev. Lett. 123, 170402, 2019.

3. Jie Zhu, Meng-Jun Hu, Shuming Cheng*, Michael J. W. Hall, Chuan-Feng Li, Guang-Can Guo, and Yong-Sheng Zhang. Experimental verification of anisotropic invariance for three-qubit states. Phys. Rev. A 99.040103.

4. Chao Zhang, Shuming Cheng*, Li Li, Qiu-Yue Liang, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Michael J. W. Hall, Howard M. Wiseman, and Geoff J. Pryde. Experimental validation of quantum steering ellipsoids and tests of volume monogamy relations. Phys. Rev. Lett. 122, 070402, 2019.

5. Shuming Cheng and Lijun Liu. Monogamy relations for nonclassical correlations of multi-qubit states. Phys. Lett. A. 382, 1716, 2018. 

6. Shuming Cheng and Michael J. W. Hall. Anisotropic invariance and the distribution of quantum correlations. Phys. Rev. Lett. 118, 010401, 2017. 

7. Shuming Cheng, Antony Milne, Michael J. W. Hall, and Howard M. Wiseman. Volume monogamy of quantum steering ellipsoids for multiqubit systems. Phys. Rev. A 94, 042105, 2016. 

8. Lijun Liu, Shuming Cheng, and Zairong Xi. Characteristic polynomial presentations for qubits. Journal of System Science and Mathematical Science, 36 (3): 453-460, 2016.

9. Shuming Cheng and Michael J. W. Hall. Complementarity relations for quantum coherence. Phys. Rev. A 92, 042101, 2015. 

10. Lijun Liu, Shuming Cheng, Bo Qi, Zairong Xi, and Daoyi Dong. Precision limit of atomic magnetometers in the presence of spin-destruction collisions. Journal of Physics B: Atomic, Molecular and Optical Physics, 48, 035502, 2015. 

11. Lijun Liu, Bo Qi, Shuming Cheng, and Zairong Xi. High precision estimation of inertial rotation via the extended Kalman filter. The European Physical Journal D, 69 (11): 1-6, 2015.

12. Lijun Liu, Shuming Cheng, Zairong Xi and Bo Qi. The influence of spin-destruction collisions on the precision of atomic SERF magnetometer. Journal of System Science and Mathematical Science, 34 (11): 1401-1410, 2014.

1.Quantum Science and Technology、 Journal of Physics A、 Journal of Mathematical Physics、和 Quantum Information Processing 等学术杂志审稿人。

2. Journal of Physics A 2019年优秀审稿人。

3. 参与翻译科普书籍《爱因斯坦也犯错：天才的一生》。