Publications (13)
A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing
Quanjun Lang, Jianfeng Lu
Quantum superoperator learning is a pivotal task in quantum information science, enabling accurate reconstruction of unknown quantum operations from measurement data. We propose a…
Small noise analysis for Tikhonov and RKHS regularizations
Quanjun Lang, Fei Lu
Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open.…
Data adaptive RKHS Tikhonov regularization for learning kernels in operators
Fei Lu, Quanjun Lang, Qingci An
We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient…
Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals
Fabrice Baudoin, Quanjun Lang, Yannick Sire
We investigate regularity properties of some non-local equations defined on Dirichlet spaces equipped with sub-gaussian estimates for the heat kernel associated to the generator. W…
Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel
Quanjun Lang, Xiong Wang, Fei Lu +1
Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. Given data consisting of multiple trajectories, we jointly infer the (weighted…
Powers Of Generators On Dirichlet Spaces And Applications To Harnack Principles
Fabrice Baudoin, Quanjun Lang, Yannick Sire
We provide a general framework for the realization of powers or functions of suitable operators on Dirichlet spaces. The first contribution is to unify the available results dealin…