This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the relationship between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the output. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings.

翻译：本文报告了一种基于支持量子力学的数学形式主义的监督机器学习新方法。 这种方法使用预测量量测量作为建立预测功能的一种方法。 具体地说, 输入量和产出变量之间的关系是双面量系统的现状。 状态是从培训样本中估计出来的,通过产生密度矩阵的平均过程。 新样本标签的预测是通过与操作员一起对双面系统进行预测性测量,由新的输入样本编制,并使用部分痕迹来获取代表输出的子系统的状况。 该方法可以被视为贝叶斯语推论分类的概括化和以内核为基础的学习方法的一种类型。 该方法的一个显著特征是,它不需要通过优化来学习任何参数。 我们用不同的2-D分类基准问题和不同的量子信息编码来说明该方法。