Simulating stochastic processes with quantum devices

The simulation of stochastic processes is a key task in quantitative sciences and thus has been studied theoretically and practically in many contexts. For stationary discrete-valued stochastic processes, the provably optimal classical simulation models are so-called ϵ-machines. These models utilize the fact that all necessary information about a process’s past can be stored within some internal memory states related to the model’s memory requirement. ϵ-machines are classically optimal, meaning that they require only a minimal number of internal states. However, these simulation models are not optimal in the quantum setting, i.e., when the models have access to quantum devices. Yet, current approaches to obtain quantum simulation models are insufficient, since they rely on having an ϵ-machine already and utilize classical computers only, which eliminates any quantum advantage. A real-world scenario, however, requires obtaining such simulation models based only on data and without a priori knowledge of the underlying stochastic process. The aim of this project is to use machine learning techniques to learn such quantum simulation models based only on data and further investigate the possibility of extending these approaches toward continuous, multivariate, and non-stationary processes.