Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum inspired generative models, such as Born machines based on the matrix product state framework, have demonstrated remarkable capabilities in unsupervised learning tasks. This study advances the Born machine paradigm by introducing trainable token embeddings through positive operator valued measurements, replacing the traditional approach of static tensor indices. Key technical innovations include encoding tokens as quantum measurement operators with trainable parameters and leveraging QR decomposition to adjust the physical dimensions of the MPS. This approach maximizes the utilization of operator space and enhances the model's expressiveness. Empirical results on RNA data demonstrate that the proposed method significantly reduces negative log likelihood compared to one hot embeddings, with higher physical dimensions further enhancing single site probabilities and multi site correlations. The model also outperforms GPT2 in single site estimation and achieves competitive correlation modeling, showcasing the potential of trainable POVM embeddings for complex data correlations in quantum inspired sequence modeling.

翻译：生成模型旨在学习数据背后的概率分布，从而能够生成新的、真实的样本。量子启发生成模型，例如基于矩阵乘积态框架的玻恩机器，已在无监督学习任务中展现出卓越的能力。本研究通过引入基于正算子值测量的可训练词元嵌入，取代了传统的静态张量索引方法，从而推进了玻恩机器的范式。关键技术创新包括：将词元编码为具有可训练参数的量子测量算子，并利用QR分解来调整MPS的物理维度。该方法最大限度地利用了算子空间，并增强了模型的表达能力。在RNA数据上的实证结果表明，与独热编码相比，所提方法显著降低了负对数似然，更高的物理维度进一步提升了单点概率和多位点相关性。该模型在单点估计方面也优于GPT2，并实现了具有竞争力的相关性建模，展示了可训练POVM嵌入在量子启发的序列建模中处理复杂数据相关性的潜力。