Quantum computers have the potential to expand the utility of lattice gauge theory to investigate non-perturbative particle physics phenomena that cannot be accessed using a standard Monte Carlo method due to the sign problem. Thanks to the qubit, quantum computers can store Hilbert space in a more efficient way compared to classical computers. This allows the Hamiltonian approach to be computationally feasible, leading to absolute freedom from the sign-problem. How concrete and extensive this possibility is should be investigated with new algorithms and through direct simulations. In this talk we briefly report the use of D-Wave and IBM quantum hardware to study the energy spectrum and the time evolution of a SU(2) pure gauge lattice theory in its Hamiltonian formulation. Since the available quantum hardware are still noisy and with few resources we rationed them by block diagonalizing the Hamiltonian and by combining gates together to minimizing the circuit length. The error was reduced by using various simple error mitigation techniques, like mitigation of measurement error, randomized compiling, zero noise extrapolation and our novel technique called Self-mitigation. The talk will be based on https://arxiv.org/abs/2103.08661 and https://arxiv.org/abs/2205.09247.