Robust and efficient quantum reservoir computing with a discrete time crystal

The rapid development of machine learning and quantum computing has placed quantum machine learning (QML) at the forefront of research. However, existing QML algorithms based on quantum variational algorithms face challenges in trainability and noise robustness. To address these challenges, we introduce a gradient-free, noise-robust quantum reservoir computing algorithm that harnesses discrete time crystal dynamics as a reservoir. We characterize the memory, nonlinear, and information scrambling capacities of the quantum reservoir, revealing their correlation with dynamical phases and nonequilibrium phase transitions. For ten-class classification, both noisy simulations and experimental results on superconducting quantum processors match ideal simulations, demonstrating that accuracy increases with system size and confirming topological robustness against noise. Our work presents the first experimental demonstration of quantum reservoir computing for image classification based on digital quantum simulation. Besides, it also experimentally demonstrates the relationship between many-body nonequilibrium dynamical phase transitions and QML performance. These findings introduce noise-robust and efficient design principles for quantum reservoir computing and broader quantum machine learning algorithms in the NISQ era.