We will recall the theory of Markovian Quantum feedback Networks, and explain some recent models with non-Markovian behaviour coming from physical requirements.

The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering, and we build on the ideas of by Bouten and van Handel to develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes Z and the measured process Y, and to this end make a distinction between what we call the input picture and the output picture.

The theory is general enough to include a modulating filter which processes the measurement readout Y before returning to the system. This opens up the prospect of applying very general engineering feedback control techniques to open quantum systems in a systematic manner, and we consider a number of specific modulating filter problems.

Bio. John E. Gough was born in Drogheda, Ireland, in 1967. He received the B.Sc. and M.Sc. in Mathematical Sciences and the Ph.D. degree in Mathematical Physics from the National University of Ireland, Dublin, in 1987, 1988 and 1992 respectively. He was reader in Mathematical Physics at the Department of Mathematics and Computing, Nottingham-Trent University, up until 2007. He then joined the Institute of Mathematics and Physics at Aberystwyth University as established chair of Mathematics. He has held visiting positions at the University of Rome Tor Vergata, EPFL Lausanne, UC Santa Barbara and the Hong Kong Polytechnic University. His research interests include quantum probability, measurement and control of open quantum dynamical systems, and quantum feedback networks.