In the Dutch energy market, the facilitation of digital communication and information exchange is essential. From monitoring real-time data of energy supply to ensuring secure energy distribution, varying applications operate together to communicate information in the energy sector. With the advancement of quantum computing technology, security threats to cryptographic algorithms may no longer be safe. While there is a need to shift towards quantum-safe solutions, there is little knowledge about quantum-safe technology and the trajectories of the Dutch energy market in the quantum era. This research aims to explore potential trajectories in the energy sector to allow better preparation for the quantum era. The results provide insights into the stakeholder and institutional layers that may require interventions to develop quantum-safe applications in the Dutch energy market. Viewing the system as a complex system and determining target areas using a Technological Innovation System (TIS) framework, data is abstracted from an extensive literature study and interviews with experts. The functions of the TIS are used as codes to analyse the interviews. The results of the desk research, literature review and expert interviews are triangulated. These results show potential for three scenarios of the Future Energy System (FES), varying in interconnectedness and decentralisation. Scenario 1 presents a simultaneous transition across the target system, scenario 2 shows a top-to-bottom approach with priority at the highest level of Internet of Energy (IoE) and scenario 3 focuses on the security of localised energy communities with a bottom-to-top approach.