Implementing quantum dimensionality reduction for non-Markovian stochastic simulation

Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly non-Markovian processes - where the future behaviour depends on events that happened far in the past - must track copious amounts of information about past observations, requiring high-dimensional memories. Quantum technologies can ameliorate this cost, allowing models of the same processes with lower memory dimension than corresponding classical models. Here we implement such memory-efficient quantum models for a family of non-Markovian processes using a photonic setup. We show that with a single qubit of memory our implemented quantum models can attain higher precision than possible with any classical model of the same memory dimension. This heralds a key step towards applying quantum technologies in complex systems modelling. Quantum technologies allow memory advantages in simulating stochastic processes, but a demonstration of this for non-Markovian processes (where the advantage would be stronger) has been missing so far. Here the authors fill this gap analytically and experimentally, using a single qubit memory to model non-Markovian processes.