Abstract: Quantum computers promise to provide a leap in our ability to numerically explore quantum field theories (QFTs). The change in nature between quantum computation and classical computation however requires us to develop new ways of understanding our QFTs which are more suitable for the former. In particular, formulations which are Hamiltonian in nature, gauge invariant, and whose Hilbert space is naturally discretized, are sought after. Furthermore, in the asymptotically free theory of Yang-Mills (YM), one would like to find a formulation which is naturally described in a basis in which the magnetic sector of the Hamiltonian, which is dominant near the continuum, is as simple as possible. In this talk we will present the solution to this problem found in 2409.13812. By simultaneously combining the fully gauge-fixed magnetic formulation found by Irian D’Andrea and her collaborators in 2307.11829 with the naturally discrete Loop-String-Hadron formulation of Jesse Stryker and collaborators 1912.06133, we complete the program started in 1509.04033 by providing a fully geometric description of the Hilbert space of SU(2) Yang-Mills as well as an algorithmic prescription for the construction of the Hamiltonian in this basis.