Quantum Observers: A NISQ Hardware Demonstration of Chaotic State Prediction Using Quantum Echo-state Networks

Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Quantum computers, which replace bits with qubits, hold the potential to overcome these limitations and increase processing power beyond classical systems. Despite this, integrating quantum computing with NNs remains largely unrealized due to challenges such as noise, decoherence, and high error rates in current quantum hardware. In this work, we propose a novel quantum circuit design and implementation algorithm that results in a dynamic quantum echo-state network (QESN). We apply classical control-theoretic response analysis to characterize the QESN, emphasizing its rich nonlinear dynamics and memory. We demonstrate that despite incorporating sparser gate weights for computational efficiency, the QESN preserves its rich dynamicity while enabling system trajectory predictions on any digital quantum computer that can implement a universal gate set. We validate our approach through a comprehensive demonstration of QESNs functioning as quantum observers, applied in both high-fidelity simulations and hardware experiments utilizing data from a prototypical chaotic Lorenz system. Our results show that the QESN can predict long time-series with persistent memory, running over 100 times longer than the median T1 and T2 of the IBM Marrakesh QPU, achieving state-of-the-art performance on superconducting hardware.