Quantum computer and computing are areas of theoretical and experimental research having a phase of growth that can generate a tectonic shift of the evolution of technology in society. The scientific and technological development in quantum research is due to a range of driving technological trajectories that are growing to solve more and more complex problems. The goal of this study is to detect emerging research fields and technological trajectories of quantum computing to explain and generalize, whenever possible, the technological characteristics of evolutionary dynamics in science and technology. Database of Scopus concerning documents and patents is used for statistical analyses to determine the growth of research fields and technological trajectories having a high potential impact in science and society. Results suggest that quantum research is driven by emerging scientific and technological trajectories given by Qubits, Quantum optics, Quantum circuit, Semiconductor quantum dots and quantum information. Overall, this study explains, whenever possible, emerging research fields and technological technologies in quantum computing that support scientific and technological change directed to future economic and social progress. Finally, technology analysis of this study can help policymakers to support the allocation of resources for all areas of Quantum Science having a high potential of growth and positive impact in science and society.