Quantum integrability and quantum computing

This award funds the research activities of Professor Rafael Nepomechie at the University of Miami. 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 accurate 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 pace. Indeed, the development and application of such devices are national priorities. The simulation of quantum systems is widely regarded as one of the most promising applications of quantum computers. Under this grant award, Professor Nepomechie will work on the simulation of quantum integrable models on quantum computers, thereby advancing the national interest in Quantum Information Science. He will also work on the foundations and applications of quantum integrability. This project is envisioned to have significant broader impacts. Professor Nepomechie will provide scientific training to the next generation of scientists through teaching and mentoring in Miami of high-school, undergraduate and graduate students, as well as in Africa at centers of the African Institute for Mathematical Sciences (AIMS). He will continue to give public lectures and engage in other outreach activities. He will continue serving on the Executive Editorial Board of Journal of Physics A and in the Editorial College of SciPost Physics. More technically, Professor Nepomechie and his coworkers will develop protocols for preparing exact many-body quantum states on a quantum computer. He will formulate an algorithm for preparing exact eigenstates of the XXZ quantum spin chain that better-exploits the integrability of the model. He will also investigate the preparation of simpler states that can be accomplished efficiently, and obtain corresponding exact matrix product state (MPS) representations. He will consider su(2)-invariant qudit systems, and investigate their fast-forwarding. Professor Nepomechie will also continue working on the foundations and applications of quantum integrability. Together with his coworkers, he will develop Q-systems for solving Bethe equations, and investigate noninvertible symmetries in integrable models. 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.