Torsten Zache, IQOQI & Center for Quantum Physics, University of Innsbruck

Non-abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. In this talk, I will present an approach where gauge fields, discretized in spacetime, are represented by qudits and are time-evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware-efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as error-tolerant holonomic operations supported by a Rydberg blockade mechanism. Our proposal is illustrated for a minimal digitization of non-abelian gauge fields via a finite subgroup of SU(2).