Towards quantum simulating non-Abelian lattice gauge theories

There has been revived interest in the Hamiltonian-formulation of lattice gauge theories given the improving prospects of quantum simulation and quantum computation. In recent years we saw a surge in efforts towards the quantum simulation of gauge theories, specifically for the Schwinger model. However, generalizing those for non-Abelian gauge theories is nontrivial because of non-Abelian Gauss' law constraint. We discuss a novel Loop-String-Hadron (LSH) formalism of SU(2) gauge theory that solves the Gauss' law exactly and brings non-Abelian gauge theories to the same footing as the Schwinger model. In lower dimensions, LSH formalism exhibits several computational benefits over any other variant of Hamiltonian lattice gauge theories present in literature in the context of classical computation. From a quantum computational perspective, LSH seems promising for both digital and analog simulations. We perform digitization of LSH Hilbert space and construct an oracle for identifying the physical states of SU(2) gauge theory in any dimension.  We also propose an analog quantum simulator for simulating real-time dynamics of $(1+1)$-d non-Abelian gauge theory well within the existing capacity of ultracold atom experiments.