Hatem Barghathi (U. Tennessee) A Compact Unary Coding for Bosonic States We introduce a unary coding of bosonic occupation states based on the famous "balls and walls" counting for the number of configurations of N indistinguishable particles on L distinguishable sites. Each state is represented by an integer with a human readable bit string that has a compositional structure allowing for the efficient application of operators that locally modify the number of bosons. By exploiting translational and inversion symmetries, we identify a speedup factor of order L over current methods when generating the basis states of bosonic lattice models. The unary coding is applied to a one-dimensional Bose-Hubbard Hamiltonian with up to L=N=20, and the time needed to generate the ground state block is reduced to a fraction of the diagonalization time. For the ground state symmetry resolved entanglement, we demonstrate that variational approaches restricting the local bosonic Hilbert space could result in large relative errors.