Quantum MPPI control achieves quadratic speedup in rare-event regimes

Model Predictive Path Integral (MPPI) control is a powerful sampling-based method for nonlinear control, but it can require an enormous number of classical rollouts when events are rare or accuracy demands are high. In a new arXiv paper (2607.28851), Goutam Das and Takashi Tanaka show how to reformulate each component of the finite-ensemble MPPI update as a ratio of bounded path expectations. They construct reversible rollout oracles that encode these expectations as success probabilities, making the update directly estimable by quantum amplitude estimation.

This reformulation yields a quadratic improvement in query dependence on both accuracy and rare-event desirability compared to classical Monte Carlo—matching known lower bounds for the underlying scalar problem below the exhaustive-evaluation threshold. The coordinatewise construction incurs only a linear dependence on the number of control inputs. At low temperatures, the weights concentrate on minimum-cost trajectories, connecting the limiting control to quantum minimum finding when a unique minimizer exists. The authors validate predicted scalings with a fully enumerable example and provide an operation-count model that separates query advantage from implementation advantage. The paper is 6 pages, submitted to LCSS+ACC 2027, and available on arXiv.