Forecasting Low-Dimensional Turbulence via Multi-Dimensional Hybrid Quantum Reservoir Computing

The prediction of complex dynamics remains an open problem across many domains of physics, where nonlinearities and multiscale interactions severely limit the reliability of conventional forecasting methods. Quantum reservoir computing (QRC) has emerged as a promising paradigm for information processing by exploiting the high dimensionality of the Hilbert space, where the dynamics of quantum systems take place. Here, we introduce a hybrid quantum-classical reservoir architecture capable of handling multivariate time series through quantum evolution combined with classical memory enhancement. Our model employs a five-qubit transverse-field Ising Hamiltonian with input-modulated dynamics and temporal multiplexing, enabling the encoding of input signals over multiple timescales. We apply this framework to two paradigmatic models of chaotic behavior in fluid dynamics, where multiscale dynamics and nonlinearities play a dominant role: a low-dimensional truncation of the two-dimensional Navier-Stokes equations and the Lorenz-63 system. By systematically scanning the quantum system's parameter space, we identify regions that maximize forecasting performance, as measured by the Valid Prediction Time. The observed robustness and reliable performances for both dynamical systems suggest that this hybrid quantum approach offers a flexible platform for modelling complex nonlinear time series.