Quantum computing (QC) is the next frontier in computation and has attracted a lot of attention from the scientific community in recent years. With the ever-increasing complexity of combinatorial optimization problems accompanied by a quickly growing search space, there arises a need for novel solution approaches capable of overcoming limitations of the current optimization paradigms carried out on state-of-the-art classical computers. QC provides a novel approach to help solve some of the most complex optimization problems while offering an essential speed advantage over classical methods. Complex nature of energy systems due to their structure and large number of design and operational constraints make energy systems optimization a hard problem for most available algorithms. We propose novel reformulations of energy systems optimization problems namely facility location-allocation for energy systems infrastructure development, unit commitment of electric power systems operations, and heat exchanger network synthesis into unconstrained binary optimization problems to facilitate ease of mapping and solving on quantum hardware. Several technological limitations face commercially available quantum computers, therefore, harnessing the complementary strengths of classical and quantum computers to solve complex large-scale optimization problems is of utmost importance. We further develop novel hybrid QC-based models and methods that exploit the complementary strengths of QC and exact solution techniques to overcome the combinatorial complexity when solving large-scale discrete-continuous optimization problems. The applicability of these QC-based algorithms is demonstrated by large-scale applications across scales that are relevant to molecular design, process scheduling, manufacturing systems operations, and logistics optimization. Apart from optimization, QC-based techniques can also be applied to fault diagnosis of complex chemical processes.