Tensor network approach to quantum feedback dynamics

In this talk I consider the problem of a quantum system coupled to a bosonic reservoir creating a coherent feedback loop. Since the system can be strongly correlated with the in-loop field, this is in general a highly non-Markovian quantum problem where no perturbative approach can be expected to work well. I will present the first practical approach to model this type of dynamics for general quantum systems and large delay times. Borrowing ideas from the intersection of condensed matter and quantum information theory, I will show that a formal dynamical solution can be found as the continuum limit of a tensor network, much like the recently introduced continuous matrix product states for one-dimensional field theories. This gives rise to a practical and efficient integration scheme in discrete time, which is numerically exact as the time-step goes to zero. Besides opening the possibility to study a new regime of quantum feedback control, this is also a novel application of tensor network techniques that could pave the way for a new approach to non-Markovian quantum dynamics in a broader context as well.