Simulating gauge-invariant SU(2) Yang-Mills Theory with near-term quantum computers

Quantum Simulation of the Lattice Gauge Theories is a prime candidate for useful applications on near-term quantum devices. Some abelian gauge groups have already been simulated with great success, however, non-abelian groups have seen less progress due to challenges in implementing the Gauss constraint. In this talk, we go directly to the gauge-invariant Hilbert space by implementing the constraint prior to simulations. While the resulting Hamiltonian is of greater complexity, it also provides an inherent robustness of the system with respect to gauge-transformation and a reduction in the number of qubits required for the simulation. We showcase the advantages of this method explicitly for a toy-model of coarse-grained SU(2) Yang-Mills theory in 3D and develop a variational algorithm to obtain the energy levels of the system with high accuracy even on NISQ devices.