Disordered systems and quantum algorithms: from spin glasses to neural networks

Abstract

This thesis investigates how quantum algorithms can solve disordered systems, with a focus on spin glasses and neural networks. We first introduce several examples of disordered systems and have an overview of spin glasses. Then we introduce a cyclic quantum annealing protocol on D-Wave’s 5000-qubit processor that explores deeper energy landscapes and reduces annealing time by up to 85% compared to traditional forward annealing. To address the challenge of exponentially small energy gaps, we introduce a new framework that uses cyclic quantum annealing to efficiently sample low-energy basins, cooling the ensemble with a digital cooling technique. It approaches exact ground states of large spin glasses with a scaling advantage—achieving computational complexity of 2 N/𝜷 with 𝜷=10³ compared to 𝜷=10² in the best classical methods we are aware of. Building on the basin structure in spin glasses, we propose quantum basin training for neural networks. This method surpasses classical backpropagation in scaling efficiency, and requires several times fewer epochs. Importantly, once a neural network is trained via the quantum device, it can be directly deployed on a classical hardware. Our results highlight that quantum annealing is a promising avenue for addressing the escalating computational costs of modern neural networks training. Additionally, we analyze the evolution of neural networks' energy landscapes, explain the mechanism of neural networks and why quantum dynamics accelerates its beneficial development.