Compact unary coding for bosonic states as efficient as conventional binary encoding for fermionic states

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