Quantum simulation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>QC</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mi mathvariant="normal">D</mml:mi></mml:mrow></mml:math> on

We study the Hamiltonian formulation of SU(2) Yang-Mills theory with staggered fermions in a (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>)-dimensional small lattice system. We construct a gauge-invariant and finite-dimensional Hilbert space for the theory by applying the loop-string-hadron formulation and specifically map the model to a spin system. We classically emulate digital quantum simulation and observe the real-time evolution of the single-site entanglement entropy, the fermion entanglement entropy, and the fermion pair production.