Quantum and Classical Spin-Network Algorithms for q-Deformed Kogut-Susskind Gauge Theories

Treating the infinite-dimensional Hilbert space of non-Abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we employ q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, this approach simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical spin-network algorithms for q-deformed gauge theories. To be explicit, we focus on SU(2)_{k} gauge theories with k∈N that are controlled by the deformation parameter q=e^{2πi/(k+2)}, a root of unity, and converge to the standard SU(2) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)_{k} plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-Abelian gauge theories far from equilibrium where no other methods are currently available.

Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms

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. Here we take 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 holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices.