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

2026-07-12

AI Summary

This work formulates a ℤₖ p-form gauge field Hamiltonian theory on arbitrary-dimensional cell complexes, tailored for digital quantum simulation and designed to accurately capture higher-order topological phenomena such as cosmological constant cancellation. By parameterizing the physical Hilbert space with electric flux variables and employing boundary maps, the authors derive Gauss’s law, magnetic constraints, and boundary-dressed Wilson operators, thereby establishing a unified framework that bridges higher-form gauge theories and quantum error-correcting codes. The resulting reduced model takes the form of an Ising-type plaquette Hamiltonian amenable to efficient dynamical simulation. Numerical studies on 4×4, 6×4, and 5×5 tori reveal a critical tension-to-density ratio (≈1.89) governing flux sector dynamics, confirming the model’s validity and providing a theoretical foundation for direct implementation on digital quantum hardware.

Abstract

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 $σ_p^z\prod_{\ell\in\partial p}τ_\ell^z$. A tube-cap quench compares two initial flux fillings with the same initial boundary loops. Exact diagonalization on $4\times4$, $6\times4$, and $5\times5$ 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 $(m/\varepsilon_E)_c\simeq1.89$. 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.

Problem

• p-form gauge theory
• quantum simulation
• Gauss law
• cosmological constant neutralization
• topological dynamics

Innovation

• p-form gauge theory
• digital quantum simulation
• quantum error correction
• cellular complexes
• cosmological constant neutralization