[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] As one of the successful theories in physics, quantum physics, constructed out of physical ideas and expressed mathematically, provides the required information for the development of technology by describing atomic or quantum systems. For several reasons related to the characteristics of quantum physics knowledge, students struggle with understanding the concepts forcing them to change their classical thinking. However, previous research showed that discussing quantum physics phenomena with peers helped students in problem solving, improving understanding, and constructing quantum physics knowledge. In this study, we focused on students’ knowledge construction in several different quantum physics topics with peer discussions depending on the kind of quantum physics problems and group structure. Examination of students’ tests with 45 quantum physics problems and reflection reports for four sessions during the semester indicated that the occurrence of knowledge construction is associated with group size and gender composition but not with the kind of problems. The knowledge construction condition is also related to group size, and satisfaction with knowledge and disagreements in group discussions are important for the construction of quantum physics knowledge.