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Quantum genetic algorithm (QGA) is the combination between genetic algorithm and quantum computing. In this paper, a chromosome of the standard QGA is seen as a node and the chromosome population is regarded as a network. Then the reasons for the prematurity and the stagnation of the standard QGA are analyzed from the perspective of network structure. To solve the two problems, an improved quantum genetic algorithm (IQGA) based on the small world theory is proposed. In IQGA, chromosomes encoded with qubits are divided into some sub-groups and the NW network model is introduced into the population structure. When updating chromosomes, an optimal chromosome in locality or in other sub-groups is chosen based on a certain probability as the evolution target for each chromosome. The new network structure of the chromosome population has a relatively moderate clustering coefficient and is favorable to the diversity of individual chromosomes. Tests of three classic functions prove the effectiveness and superiority of IQGA.