Bayesian Optimization by Kernel Regression and Density-based Exploration

Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the high computational complexity of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose the Bayesian Optimization by Kernel regression and density-based Exploration (BOKE) algorithm. BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and the improved kernel regression upper confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE and ensures its robustness. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.

Variational Quantum Circuits Enhanced Generative Adversarial Network

Generative adversarial network (GAN) is one of the widely-adopted machine-learning frameworks for a wide range of applications such as generating high-quality images, video, and audio contents. However, training a GAN could become computationally expensive for large neural networks. In this work, we propose a hybrid quantum-classical architecture for improving GAN (denoted as QC-GAN). The performance was examed numerically by benchmarking with a classical GAN using MindSpore Quantum on the task of hand-written image generation. The generator of the QC-GAN consists of a quantum variational circuit together with a one-layer neural network, and the discriminator consists of a traditional neural network. Leveraging the entangling and expressive power of quantum circuits, our hybrid architecture achieved better performance (Frechet Inception Distance) than the classical GAN, with much fewer training parameters and number of iterations for convergence. We have also demonstrated the superiority of QC-GAN over an alternative quantum GAN, namely pathGAN, which could hardly generate 16$\times$16 or larger images. This work demonstrates the value of combining ideas from quantum computing with machine learning for both areas of Quantum-for-AI and AI-for-Quantum.