Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to exhibit memory advantages for such tasks. Heretofore, the focus has been on lossless memory compression, wherein the advantage is typically in terms of lessening the amount of information tracked by the model, while -- arguably more practical -- reductions in memory dimension are not always possible. Here we address the case of lossy compression for quantum stochastic modelling of continuous-time processes, introducing a method for coarse-graining in quantum state space that drastically reduces the requisite memory dimension for modelling temporal dynamics whilst retaining near-exact statistics. In contrast to classical coarse-graining, this compression is not based on sacrificing temporal resolution, and brings memory-efficient, high-fidelity stochastic modelling within reach of present quantum technologies.
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