虚拟量子神经网络
Virtual quantum neural networks
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中文总结 AI 辅助
本文提出虚拟量子神经网络，通过随机采样和经典数据处理扩展优化空间至完全正映射的线性组合，提升了表达能力和噪声鲁棒性，并在量子错误缓解、二分类和基态能量估计任务中验证了其优势。
中文摘要 AI 辅助
量子神经网络是量子机器学习的一种重要模型。其训练过程涉及在参数化的量子电路族（数学上由酉算子或更一般的完全正线性映射描述）上最小化给定的损失函数。在本工作中，我们通过随机采样和经典数据处理扩展了量子神经网络的概念，将优化空间扩大至包含完全正映射的线性组合。我们提出的扩展模型称为虚拟量子神经网络，利用其扩大的优化空间实现了更高的表达能力和更强的噪声鲁棒性。这些优势在三个代表性任务中得到展示：量子错误缓解、二分类以及基态能量估计。总体而言，虚拟量子神经网络提供了一种灵活的学习范式，扩展了可实现计算的空间，并增强了近期量子硬件的应用前景。
英文摘要
Quantum neural networks are a prominent model of quantum machine learning. Their training consists in the minimization of a given loss function over a parametrized family of quantum circuits, mathematically described by unitary operators, or, more generally, completely positive linear maps. In this work, we extend the notion of quantum neural network, using random sampling and classical data processing to enlarge the optimization space in a way that includes linear combinations of completely positive maps. Our extended model, called virtual quantum neural networks, leverages its enlarged optimization space to achieve increased expressivity and improved noise robustness. These benefits are illustrated in three representative tasks: quantum error mitigation, binary classification, and estimation of ground-state energies. Overall, virtual quantum neural networks offer a flexible learning paradigm that expands the space of achievable computations and strengthens the applications of near-term quantum hardware.
发表机构
- QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（香港大学计算与数据科学学院量子信息与计算倡议）
- School of Artificial Intelligence, Wuhan University（武汉大学人工智能学院）
- Hubei Center for Applied Mathematics（湖北应用数学中心）
- Hubei Key Laboratory of Computational Science（湖北省计算科学重点实验室）
- Wuhan Institute of Quantum Technology（武汉量子技术研究院）
- School of Mathematical Sciences, Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University（复旦大学数学科学学院当代应用数学上海市重点实验室）
- Key Laboratory of Computational Physical Sciences, Ministry of Education（教育部计算物理科学研究院）
- Quantum Group, Department of Computer Science, University of Oxford（牛津大学计算机系量子研究组）
- Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
机构由 AI 辅助整理，请以论文原文为准。
