论文标题
克利福德代数，量子神经网络和广义量子傅里叶变换
Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform
论文作者
论文摘要
我们通过Clifford代数提出了量子神经网络的模型，这些模型能够捕获系统的几何特征并产生纠缠。由于其在Pauli矩阵方面的表示，Clifford代数是量子设置中多维数据分析的自然框架。讨论了激活功能和统一学习规则的实施。在此方案中，我们还提供了量子傅立叶变换的代数概括，其中包含允许执行量子机学习的其他参数。此外，已经证明了广义量子傅立叶变换的一些有趣属性。
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras are the natural framework for multidimensional data analysis in a quantum setting. Implementation of activation functions and unitary learning rules are discussed. In this scheme, we also provide an algebraic generalization of the quantum Fourier transform containing additional parameters that allow performing quantum machine learning. Furthermore, some interesting properties of the generalized quantum Fourier transform have been proved.
