The CQM team comprises over 60 researchers from diverse nationalities spanning various fields. CQM is managed by the Executive Committee, led by the CQM Scientific Coordinator. The core body of CQM is the Scientific Council, consisting of all the Ph.D. members who have been part of the unit for over a year. They hold the responsibility of electing the Scientific Coordinator, providing an opinion on the budget, and on the annual activities plan of CQM.

Additionally, CQM is overseen by the External Monitoring Committee, which consists of five external experts to CQM and the University of Madeira. This committee is accountable for evaluating CQM's activities, results, and plans, as well as offering advisory opinions on the strategic research lines, research and human resources policies, and internal dynamics of the Center.