Linking many-body physics to many-time physics: Characterising micro and macro features of non-Markovian quantum processes

A classical stochastic process is a joint probability distribution of a random variable over time. Its quantum generalisation then turns out to be a multipartite density matrix. We refer to the studies of this density matrix as many-time physics in analogy to the well-founded field of many-body physics. Here, we report a set of tools that allows us to characterise both the detailed features of a quantum process, as well as its coarse structures. The former, we show, could be used to tame correlated noise due to a quantum stochastic process. The latter, on the other hand, allows us to explore exotic features such as genuine multipartite entanglement in time. All of these tools are well-tested and shown to be highly effective on NISQ devices with real noise. Importantly, these tools have direct application for noise reduction for NISQ devices and studying facets of complex quantum processes.