p-Form Gauge Dynamics and Digital Quantum Simulation - Flux and Cosmological Constant Neutralization

I develop a Hamiltonian framework for {mathbb Z}_k p-form gauge fields on arbitrary oriented cell complexes in arbitrary dimensions. Gauge qudits are defined by p-cells, charged boundary qudits by (p-1)-cells, Gauss-law generators by boundary map partial_p, and magnetic checks by partial_p+1. The same cellular structure produces local dressed Wilson operators, and at k=2 a Calderbank-Shor-Steane check complex relevant to quantum error correction. I then specialize to p=2, k=2, where the magnetic 3-cell term is absent and the one-form Gauss-law can be solved exactly. The physical Hilbert space is parameterized by plaquette electric-flux variables, while the link configuration is reconstructed as the dynamical boundary of the evolving flux domains. The reduced Hamiltonian is an Ising-type plaquette model, where its local transverse-field term is the physical image of the boundary-dressed Wilson operator σ_p^zprod_{ellinpartial p}τ_ell^z. A tube-cap quench compares two initial flux fillings with the same initial boundary loops. Exact diagonalization on 4times4, 6times4, and 5times5 tori finds that the cap loses 20-37\% of its occupied-flux area, while the tube remains nearly pinned. A finite-size scaling locates a dynamical crossover of tension-to-density ratio near \(m/varepsilon_E\)_csimeq1.89. The unreduced plaquette-plus-link encoding provides local Gauss-law checks and a direct digital implementation, while the reduced plaquette-only Hamiltonian supplies the exact benchmark. The result places the specific top-form discharge and the cosmological constant neutralization calculation inside a general higher-form Hamiltonian and coding framework.