The quantum-many body problem appears in many fields of science and dictates the behavior of many systems ranging from nanoscale materials, to quantum dots, to chemical structure and bonding, to atomic nuclei. Scientists across these fields have found that predictive theory in these complex systems often requires the application of high-performance computing and advanced computational techniques to the problem of interest. The beauty of the quantum many-body problem in nuclei is especially pronounced as we experimentally and theoretically probe regimes of very short-lived and rare isotopes. Many of these isotopes are hard to make in the laboratory and yet some of them play important roles in the production of ordinary elements during stellar burn and explosions and other applications.

In this talk, I will assess where we stand today in computationally solving the nuclear problem and how future rare isotope facilities will impact our understanding of nuclei. I will discuss the science that goes into and comes out of the nuclear problem, and then turn to the numerical implementations of coupled-cluster theory for the problem. Specific to the nuclear problem is the presence of a real three-body force which is computationally represented by six-dimensional tensor. Both memory and communications become issues as one begins to scale up the underlying coupled-cluster algorithms to thousands of processors. Another interesting feature of the nuclear problem is weak binding that occurs in very unstable nuclei. When the single-particle continuum is present, the nuclear Hamiltonian becomes complex. I also will describe our work to solve the complex coupled-cluster problem in the presence of complex interactions.