Matrix-product-state methods for non-Markovian models

When an open quantum system is strongly coupled to a structured environment, describing the dynamics of that system becomes a challenging problem.   Moreover, traditional approaches, based on time evolution of the reduced density matrix are generally not able to correctly calculate higher-order or multi-time correlations.  I will review recent progress that addresses both these issues, by showing how the time evolution of the system can be efficiently simulated using tensor network methods [1].  Such a tensor network naturally leads one to consider the process tensor (PT), an object which encodes all multi-time correlations of the reservoir [2].  A key insight is that one can construct efficient MPO representations of the PT.  This idea makes possible many otherwise challenging tasks, including optimisation of non-Markovian systems [3] (requiring repeated simulation of the dynamics),  and modelling the non-Markovian dynamics of many-body open quantum systems [4,5]. It also prompts identification of alternate algorithms to constrcut an MPO form of the PT [6].   

The code underpinning this work is publicly available [7], and we are keen to help support other researchers in using this approach.