The increasing scale of projects in civil engineering industries leads to the increase of the amount and complexity of data that need to be treated and calculated. As a new non-traditional way of computing, quantum computing shows extremely powerful capabilities in huge data analysis and processing. In this research we focus on optimizing civil engineering construction scheduling using quantum genetic algorithms which have the outstanding performance in optimization and data processing, to create the possibility of dealing with civil engineering problem with quantum computing. This research consists of an extensive literature study that includes genetic algorithms, quantum genetic algorithms and construction scheduling. Existing applications of optimized design with genetic algorithms and quantum genetic algorithms are the theoretical basis for the hypothesis. Based on the theoretical research, an improved quantum genetic algorithm which is used for construction scheduling optimization design with the constraints of time and human resourcing is established and named as AQGA (A quantum genetic algorithm). A null hypothesis is taken: AQGA cannot help to improve the optimization design in civil engineering construction scheduling. Then a case study is done with AQGA: through the analogy with flow-shop scheduling, unit construction scheduling is chosen to be processed with AQGA. At the end of the case study, the flowchart of unit construction optimized design with improved quantum genetic algorithm AQGA is given, unit construction optimized design is realized through the improved quantum genetic algorithm There are some constraints and limitations in the study and research. For example there are simplified and idealized assumptions since a realistic simulation cannot be realized because there is no available quantum computer to run the simulation. But the unit construction scheduling optimize problem is expressed in quantum computing language. It is expected to be a starting point for future application of quantum genetic algorithms within construction scheduling in civil engineering projects and even more broad, quantum computing within civil engineering.