The realization of quantum complex-valued backpropagation neural network in pattern recognition problem

The paper presents the approach of the quantum complex-valued backpropagation neural network or QCBPN. The challenge of our research is the expected results from the development of the quantum neural network using complex-valued backpropagation learning algorithm to solve classification problems. The concept of QCBPN emerged from the quantum circuit neural network research and the complex-valued backpropagation algorithm. We found that complex value and the quantum states share some natural representation suitable for the parallel computation. The quantum circuit neural network provides a qubit-like neuron model based on quantum mechanics with quantum backpropagation-learning rule, while the complex-valued backpropagation algorithm modifies standard backpropagation algorithm to learn complex number pattern in a natural way. The quantum complex-valued neuron model and the QCBPN learning algorithm are described. Finally, the realization of the QCBPN is exploited with a simple pattern recognition problem.