Many-body nuclear physics is the bridge that takes us from the fundamental laws governing individual nucleons to understanding how groups of them interact together to form the nuclei that lie at the heart of all atoms-the building blocks of our universe. Many powerful techniques of classical computation have been developed over the years in order to study ever more complex nuclear systems. However, we seem to be approaching the limits of such classical techniques as the complexity of many-body quantum systems grows exponentially. Yet, the recent development of quantum computers offers one hope as they are predicted to provide a significant advantage over classical computers when tackling problems such as the quantum many-body problem. In this thesis, we focus on developing and applying algorithms to tackle various many-body nuclear physics problems that can be run on the near-term quantum computers of the current noisy intermediate-scale quantum (NISQ) era. As these devices are small and noisy, we focus our algorithms on various many-body toy models in order to gain insight and create a foundation upon which future algorithms will be built to tackle the intractable problems of our time. In the first part, we tailor current quantum algorithms to efficiently run on NISQ devices and apply them to three pairing models of many-body nuclear physics, the Lipkin model, the Richardson pairing model, and collective neutrino oscillations. For the first two models, we solve for the ground-state energy while for the third, we simulate the time evolution and characterize the entanglement. In the second part, we develop novel algorithms to increase the efficiency and applicability of current algorithms on NISQ devices. These include an algorithm that compresses circuit depth to allow for less noisy computation and a variational method to prepare an important class of quantum states. Error mitigation techniques used to improve the accuracy of results are also discussed. All together, this work provides a road map for applications of the quantum computers of tomorrow to solve what nuclear phenomena mystify us today.
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