多值量子神经元
Multi-Valued Quantum Neurons
AI总结：
本文提出多值量子神经元，基于复数域多值阈值逻辑，训练简化为沿单位圆移动，构建的量子神经网络收敛快、功能强，可用于分析量子系统能谱及实际应用。
摘要：
多值量子逻辑被系统地表述，使得真值被自然地表示为位于单位圆上的唯一单位根。因此，多值量子神经元（MVQN）基于复数域上的多值阈值逻辑原理。MVQN的训练被简化为沿单位圆的移动。基于多值量子神经元的量子神经网络（QNN）可以用复数权重、输入和输出（由单位根编码）以及一个将复平面映射到单位圆的激活函数来构建。与具有相同神经元和层数的基于二进制输入的量子神经网络相比，此类神经网络具有更快的收敛速度和更高的功能。我们的构建可用于分析量子系统的能谱。利用由光的轨道角动量（OAM）或多能级系统（如分子自旋量子比特）构建的量子神经网络，可以找到潜在的实际应用。
英文摘要：
The multiple-valued quantum logic is formulated systematically such that the truth values are represented naturally as unique roots of unity placed on the unit circle. Consequently, multi-valued quantum neuron (MVQN) is based on the principles of multiple-valued threshold logic over the field of complex numbers. The training of MVQN is reduced to the movement along the unit circle. A quantum neural network (QNN) based on multi-valued quantum neurons can be constructed with complex weights, inputs, and outputs encoded by roots of unity and an activation function that maps the complex plane into the unit circle. Such neural networks enjoy fast convergence and higher functionalities compared with quantum neural networks based on binary input with the same number of neurons and layers. Our construction can be used in analyzing the energy spectrum of quantum systems. Possible practical applications can be found using the quantum neural networks built from orbital angular momentum (OAM) of light or multi-level systems such as molecular spin qudits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
