Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These networks are used to approximate high-order tensors by contracting tensors with lower ranks. Originally developed for simulating quantum systems, tensor networks have become integral to quantum computing and, by extension, to QML. Their ability to efficiently represent and manipulate complex, high-dimensional data makes them suitable for various machine learning tasks within the quantum realm. Here, we present a matrix product state (MPS) model, where the MPS functions as both a classifier and a generator. The dual functionality of this novel MPS model permits a strategy that enhances the traditional training of supervised MPS models. This framework is inspired by generative adversarial networks and is geared towards generating more realistic samples by reducing outliers. Additionally, our contributions offer insights into the mechanics of tensor network methods for generation tasks. Specifically, we discuss alternative embedding functions and a new sampling method from non-normalized MPSs.

翻译：量子机器学习是一个快速发展的领域，它融合了量子计算原理与机器学习技术。张量网络是该领域强大的数学框架之一，通过收缩低秩张量来逼近高阶张量。张量网络最初用于模拟量子系统，现已发展成为量子计算及量子机器学习的重要组成部分。其高效表示和操作复杂高维数据的能力，使其适用于量子领域的各类机器学习任务。本文提出一种矩阵乘积态模型，该模型兼具分类器与生成器的双重功能。这种新型MPS模型的双重特性为改进传统监督式MPS模型训练提供了新思路。该框架受生成对抗网络启发，旨在通过减少异常值生成更逼真的样本。此外，我们的研究为张量网络在生成任务中的机制提供了新见解，具体探讨了替代嵌入函数以及非归一化MPS的新采样方法。