To forecast the future, we look to the past. Past information of use constitutes the “predictive features” of the data. Effective forecasting leverages these features, requiring that we store information; meanwhile, efficiency demands that we find the most parsimonious means of doing so. A promising development in this direction is to make use of quantum technologies to encode this information into quantum states, providing compression advantages over corresponding classical encodings that can exhibit extreme scalings. Our work provides a means to deploy these extreme advantages to a broader range of processes. Since time is a continuous parameter, tracking its progression to higher precision requires increased memory. When dealing with temporal information, classical encodings coarse grain into finite-sized time steps, limiting the accuracy that may be achieved. We introduce a quantum analog of coarse graining that trims down the underlying quantum memory state space, rather than the degrees of freedom of the process directly. This offers extreme dimension reduction in the memory, enabling high-fidelity quantum simulation of stochastic dynamics with low memory dimension.

With the widespread use of stochastic modeling across the quantitative sciences, our work highlights the potential for quantum technologies to impact a diverse spectrum of fields. Moreover, such quantum-compression advantages are of a fundamentally different—yet complementary—nature to typical quantum advantages, by offering reductions in a spatial complexity rather than a temporal complexity speed-up. Further, the advantage can manifest even for quantum memories of only a few qubits, presenting the opportunity for imminent experimental implementations.