Model Predictive Path Integral Control as a Quantum Query Problem

Model predictive path integral (MPPI) control computes its inputs as cost-weighted averages over simulated trajectories. However, it typically requires many simulations, especially when low-cost trajectories are rare. We therefore formulate this computation as a quantum query problem. By replacing Gaussian input perturbations with random signs, we express the MPPI update as a ratio of averages over a finite set of perturbation sequences. We then construct quantum circuits that encode these averages as measurement probabilities, which allows quantum amplitude estimation to compute the update with fewer queries than classical sampling. Numerical examples confirm the predicted query scalings and show that a quantum advantage requires many perturbation sequences.