随着信息技术的高速发展,全球数据总量每年以指数规模增长，这使得经典机器学习算法在未来处理大数据时将面临计算性能方面的巨大挑战。量子计算在解决某些特定问题时相比经典计算具有显著的加速效果，而量子算法的设计是该领域研究的难点问题。本项目研究解决若干机器学习问题的量子算法，包括：①设计针对非稀疏数据矩阵、包含岭回归参数确定方案的量子岭回归算法；②设计以经典信息形式输出模型参数的量子逻辑回归算法；③设计基于主成分分析并以量子并行方式输出低维数据的量子降维算法；④设计量子条件随机场模型及相应的量子训练算法。与现有经典算法相比，本项目所提算法预期将在特定条件下实现指数加速效果。项目成果有望对未来量子计算在机器学习领域的应用提供重要参考。

With rapid development of information technology, global data grows exponentially every year, which poses great challenges to the computational performance of classical machine learning algorithms for tackling big data in the future. Quantum computing has shown significant speedup over classical computing for solving certain problems, but it remains to be difficult to design quantum algorithms. This project studies quantum algorithms for several important machine learning problems, including: (1) designing a quantum ridge regression algorithm for handling non-sparse data matrices that provides a procedure for determining the ridge parameter; (2) designing a quantum logistic regression algorithm that outputs classical model parameters; (3) designing a principal component analysis based quantum dimensionality reduction algorithm that in quantum parallel outputs the projected lower-dimensional data points; (4) constructing a quantum conditional random field model and designing a corresponding quantum training algorithm. All the proposed quantum algorithms are expected to achieve exponential speedup over the classical counterparts under certain conditions. The achievements of this project are promising to serve as important references for future applications of quantum computing in the field of machine learning.