QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning
This provides a robust advancement for quantum computing practitioners by accelerating gradient-based optimization in applications like quantum chemistry and machine learning, though it appears incremental as it combines existing theories into a novel framework.
The paper tackles the problem of linearly increasing gradient calculation complexity in quantum optimization by introducing QuACK, a framework that bridges Koopman operator theory with natural gradient methods, resulting in accelerations of over 200x in overparameterized regimes, 10x in smooth regimes, and 3x in non-smooth regimes.
Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman operator theory, which has found utility in applications because it allows for a linear representation of nonlinear dynamical systems, 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), a novel framework that leverages an alternating algorithm for efficient prediction of gradient dynamics on quantum computers. We demonstrate QuACK's remarkable ability to accelerate gradient-based optimization across a range of applications in quantum optimization and machine learning. In fact, our empirical studies, spanning quantum chemistry, quantum condensed matter, quantum machine learning, and noisy environments, have shown accelerations of more than 200x speedup in the overparameterized regime, 10x speedup in the smooth regime, and 3x speedup in the non-smooth regime. With QuACK, we offer a robust advancement that harnesses the advantage of gradient-based quantum optimization for practical benefits.