Multi-valued Quantum Neurons

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.