Carbon nanotubes, quintessentially one-dimensional quantum objects, possess a variety of electrical, optical, and mechanical properties that are suited for developing devices that operate on quantum mechanical principles. The states of one-dimensional electrons, excitons, and phonons in carbon nanotubes with exceptionally large quantization energies are promising for high-operating-temperature quantum devices. Here, we discuss recent progress in the development of carbon-nanotube-based devices for quantum technology, i.e., quantum mechanical strategies for revolutionizing computation, sensing, and communication. We cover fundamental properties of carbon nanotubes, their growth and purification methods, and methodologies for assembling them into architectures of ordered nanotubes that manifest macroscopic quantum properties. Most importantly, recent developments and proposals for quantum information processing devices based on individual and assembled nanotubes are reviewed.