We develop a theory of proportional-integral (PI) feedback control for quantum systems, and demonstrate its utility in two canonical state stabilization problems in quantum information.

Feedback control is a general approach to engineering reliability and stability in many modern technologies. PI feedback is the most common and useful type of control in classical systems, and we extend this essential engineering tool to the quantum domain.

For details see "Quantum proportional-integral (PI) control", Hui Chen, Hanhan Li, Felix Motzoi, Leigh Martin, K. Birgitta Whaley, Mohan Sarovar. arXiv:2007.13853.