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For training of process neural networks based on the orthogonal basis expansion, it is difficult to converge for BP algorithm as more parameters. Aiming at the issue, this paper proposes a solution based on quantum genetic algorithm with double chains. Firstly, the number of genes is determined by the number of weight parameters, quantum chromosomes are constructed by qubits, and the current optimal chromosome is obtained with the help of colony assessment. Secondly, taking each qubit in this optimal chromosome as the goal, individuals are updated by quantum rotation gate, and mutated by quantum non-gate to increase the diversity of population. In this method, each chromosome carrying two chains of genes, therefore it can extend ergodicity for solution space and accelerate optimization process. Taking the pattern classification of two groups of two-dimensional trigonometric functions as an example, the simulation results show that the method not only has fast convergence, but also good optimization ability.