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Quantum optimization, a key application of quantum computing, hastraditionally been stymied by the linearly increasing complexity of gradientcalculations with an increasing number of parameters. This work bridges the gapbetween Koopman operator theory, renowned for its success in predictingnonlinear dynamics, and natural gradient methods in quantum optimization,leading to a significant acceleration of gradient-based quantum optimization.We present Quantum-circuit Alternating Controlled Koopman learning (QuACK), anovel framework that leverages an alternating algorithm for efficientprediction of gradient dynamics on quantum computers. We demonstrate QuACK'sremarkable ability to accelerate gradient-based optimization across a range ofapplications in quantum optimization and machine learning. In fact, ourempirical studies, spanning quantum chemistry, quantum condensed matter,quantum machine learning, and noisy environments, have shown accelerations ofmore than 200x speedup in the overparameterized regime, 10x speedup in thesmooth regime, and 3x speedup in the non-smooth regime. With QuACK, we offer arobust advancement that harnesses the advantage of gradient-based quantumoptimization for practical benefits.

QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning