The goal of this study is to analyze evolutionary phases of emerging technologies to improve technological forecasting and management of promising innovations. Methodology applies S-shaped models with patent data to analyze the evolutionary phases in quantum technologies. Findings reveal that the evolutionary cycle of recent quantum technologies, based on patent data, is reducing compared to older technologies originated before 1980: from about 66 to 45 years. In addition, recent quantum technologies have a growth phase of about 22 years and maturity phase of 11 years, a shorter period than technologies originated before the 1980s (having a growth phase of 40 years and a maturity phase of about 13 years). The measure of entropy in the growth phase is lower (0.64) than maturity phase (0.74): a lower diversification of technological topics and technological trajectories. Results here suggest that the evolution of emerging technologies, such as quantum technology, has a high complexity and uncertainty for rapid changes in scientific and innovation ecosystem. Results support a technological management based on an ambidexterity strategy: a) Exploitation strategy in early phase of a technology's life cycle, which is characterized by concentrated topics (lower entropy index), directed to targeted investments in specific technologies; b) structure and dynamics in the maturity phase of technology's life cycle, having diversified themes (higher entropy index), suggests a strategy of exploration for detecting the most promising technological directions for future quantum innovations among new and expanding domains for achieving and sustaining competitive advantage of firms in a world of innovation-based competition.