Quantum latent diffusion model for high-dimensional state generation
摘要
Quantum machine learning, particularly in generative modeling, is rapidly gaining traction. Within this domain, diffusion models have proven effective in generating diverse, high-quality samples. However, their application to quantum data generation remains underexplored. This paper introduces the Quantum Latent Diffusion Model (QLDM), a novel approach for generating higher-quality, higher-dimensional quantum states tailored to specific quantum data generation tasks. QLDM integrates vector quantization with a quantum autoencoder, leveraging a classical diffusion model to train on reduced-dimensional latent representations. This method enables the generation of similarly-styled quantum states from Gaussian noise and significantly alleviates the barren plateau issue. Through rigorous analytical and simulation-based evaluations, we demonstrate QLDM’s efficacy and robustness. The model significantly outperforms previous quantum diffusion approaches in generating single-class quantum states with enhanced accuracy and efficiency. Additionally, QLDM excels in generating multi-class entangled states, uncovering complex topological features of energy subspaces linked to specific Hamiltonians, and facilitating approximate state generation via shallow quantum circuits. By combining quantum and classical computational strengths, QLDM establishes itself as a powerful tool for near-term quantum generative modeling.