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

TL;DR

This paper introduces QuACK, a novel framework that uses Koopman operator learning to significantly accelerate gradient-based quantum optimization across various applications, enabling practical quantum advantage.

Contribution

It presents a new method combining Koopman theory with natural gradient techniques to speed up quantum optimization processes.

Findings

Over 200x speedup in overparameterized regimes

10x speedup in smooth regimes

3x speedup in non-smooth regimes

Abstract

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.