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In the second part of the talk, I will take a step further and discuss learning classical patterns from quantum data. In this problem, the samples are quantum states with classical labels and the predictors are quantum measurements. I will introduce a quantum counterpart of PAC as a new theoretical foundation for learning from quantum data. I will point out major difficulties arising from the quantum nature of the problem, including the no-cloning principle and measurement compatibility. Then, I will present new bounds on the quantum sample complexity of several measurement classes. I will make use of a Fourier expansion for quantum operators on qubits and present the quantum low-degree algorithm.
About the speaker
Mohsen Heidari is currently a postdoctoral research associate at the Center for Science of Information, NSF Science & Technology Center at Purdue University. He obtained a Ph.D. degree in Electrical Engineering in 2019 and an M.Sc. degree in Applied Mathematics in 2017, both from the University of Michigan. Before that, he obtained his B.Sc. and M.Sc. degree in Electrical Engineering from the Sharif University of Technology in 2011 and 2013, respectively. Mohsen’s research interests lie in machine learning, information theory, and quantum information theory.