# Quantum Reservoir Network

High-dimensional PDE forecasting on unstructured meshes has run on superconducting quantum processors for the first time. A graph autoencoder compresses mesh fields into a low-dimensional latent state, a fixed, untrained quantum reservoir network supplies features, and a classical linear readout predicts the next state; on a 33,824-cell cylinder flow and a Gray–Scott reaction–diffusion problem, adding those features lowers normalized root mean square error by roughly 21–43% for one-step and pressure-observer prediction against a linear baseline on the same latent space, with the pressure observer demonstrated only on the 26-qubit cylinder configuration and the 52-qubit hardware used for Gray–Scott one-step forecasting.

High-dimensional PDE forecasting on unstructured meshes has run on superconducting quantum processors for the first time. A graph autoencoder compresses mesh fields into a low-dimensional latent state, a fixed, untrained quantum reservoir network supplies features, and a classical linear readout predicts the next state; on a 33,824-cell cylinder flow and a Gray–Scott reaction–diffusion problem, adding those features lowers normalized root mean square error by roughly 21–43% for one-step and pressure-observer prediction against a linear baseline on the same latent space, with the pressure observer demonstrated only on the 26-qubit cylinder configuration and the 52-qubit hardware used for Gray–Scott one-step forecasting.