NSF Award
2310594
This award funds the research activities of Professor Rafael Nepomechie in the Department of Physics at the University of Miami.<br/><br/>This project lies at the intersection of two important developments. On the one hand, the formulation of the Standard Model of elementary particles is one of the greatest scientific accomplishments of the 20th century. However, this model, as well as many other mathematical models, cannot be used to make accurate predictions of processes involving strong interactions, as the corresponding equations become too difficult to solve. So-called quantum integrable models lie in the "sweet spot” of theoretical physics: they are sufficiently complicated to describe interesting physics, yet they are sufficiently simple to allow for exact analytical computations of some quantities of physical interest. Integrability has therefore become one of the main guiding principles in contemporary theoretical physics. On the other hand, quantum computers, which operate on quantum bits (unlike conventional computers, which operate on 0's and 1's), are advancing at an astonishing rate. Indeed, the development and application of such devices are national priorities. The simulation of quantum systems is widely regarded as one of the best shots at an economically useful application of quantum computers. Under this grant award, Professor Nepomechie will work on the simulation of quantum integrable models on quantum computers. He will also work on the foundations and applications of quantum integrability. This project is also envisioned to have significant broader impacts. Professor Nepomechie will provide scientific training to the next generation of scientists through teaching and mentoring, reaching Miami high-school, undergraduate, and graduate students, as well as students in Africa at centers of the African Institute for Mathematical Sciences (AIMS). He will also continue to give public lectures and engage in other outreach activities, and will continue serving on the Editorial Board of Journal of Physics A and in the Editorial College of SciPost Physics.<br/><br/>More technically, Professor Nepomechie and his coworkers will develop algorithms for preparing Dicke states and their generalizations on quantum computers, and explore their properties. These highly-entangled states are the starting points of some algorithms for preparing Bethe states, and are also of interest in their own right. He will also develop algorithms for preparing exact eigenstates of integrable models. Professor Nepomechie will also continue working on the foundations and applications of quantum integrability. Together with coworkers in Europe, he will investigate integrable quantum spin chains whose continuum limits are described by so-called black-hole conformal field theories, with non-compact degrees of freedom. He will also work on computations of bipartite entanglement entropies, the Quantum Spectral Curve (QSC), and algebraic Bethe ansatz for higher-rank chains.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
