Treating the infinite-dimensional Hilbert space of non-abelian gauge theories
is an outstanding challenge for classical and quantum simulations. Here, we
introduce q-deformed Kogut-Susskind lattice gauge theories, obtained by
deforming the defining symmetry algebra to a quantum group. In contrast to
other formulations, our proposal 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 (SNAQs). To be explicit, we focus on SU(2)k
gauge theories, that are controlled by the deformation parameter k 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.Comment: 5+4 pages, 4+1 figure