Realization of quantum data assimilation for a two-dimensional quasi-geostrophic model based on a coherent Ising machine

Data assimilation (DA), vital for numerical weather prediction and Earth system modeling, struggles with escalating computational demands from complex environmental datasets. We introduce a quantum-inspired DA (QDA) framework using coherent Ising machines (CIMs): an optical solver based on the quantum squeezing effect, specialized in solving combinatorial optimization problems. The QDA method overcomes qubit limitations with domain decomposition and reformulates a classical three-dimensional variational assimilation (3D-VAR) into a quadratic unconstrained binary optimization (QUBO) problem mapped to an optical Ising Hamiltonian. Validated on a 512D quasi-geostrophic model, numerically simulated QDA achieves lower root mean square error than the classical method after 120 assimilation cycles. Single-assimilation cycle optical experiments show that QDA operates at 9.5% (25.31 ms) of the classical 3D-VAR runtime (266.4 ms), yielding a 10.5× speedup while maintaining accuracy. This demonstrates the potential of CIMs to revolutionize high-resolution environmental forecasting through energy-efficient, real-time assimilation, bridging quantum photonics and geophysics.