Application of CS in weak signal quantum measurement and protein structure calculation

It has been more than 15 years since the compressed sensing (CS) theory was put forward in 2006. The CS theory has been successfully applied and developed in many classical fields such as the single-pixel camera, CT imaging and radar imaging system, but there is still much space for its applications in quantum and biological system. In this paper, the basic knowledge of CS theory and its application/development history are briefly introduced. Then a review is given on a series of achievements in the CS theory applied in quantum precision measurement and biological system, mainly obtained by the Center for Quantum Technology Research in Beijing Institute of Technology (BIT). The review covers several different topics including the measurement and imaging in extremely weak signals, the density matrix calculation for multi-body quantum state tomography and the protein structure reconstruction from matrix completion theory, which is developed based on the CS theory. With the above reviews, we show that the CS theory has great potential for further application, not only in weak signal detection, but also in quantum calculation and even the research on bio-macromolecules. In the end, the summary and outlook are given on the future developments and applications of the CS theory.