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 SUo2THORNk gauge theories with k is an element of N that are controlled by the deformation parameter q = e(2 pi i/(k+2)), a root of unity, and converge to the standard SU(2) Kogut-Susskind model as k -> infinity. 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 highenergy physics and paves the way for quantum simulations of non-Abelian gauge theories far from equilibrium where no other methods are currently available.