Integration of IBM's Non-Abelian Fourier Transform with the Five-Dimensional Time-Delay Field Model: Quantum Simulation of τ -Mode Resonances at 5–6 TeV

This dataset and manuscript present the first integration of IBM’s Non-Abelian Fourier Transform (NAFT) algorithm with the Five-Dimensional Time-Delay Field (TDF) model, a causal scalar-field framework predicting a narrow spin-0 resonance near 5–6 TeV.
Using Quantum Phase Estimation (QPE) circuits implemented in Qiskit, we encode the delay-phase τ(x,t) as a compact U(1) operator and extract energy eigenvalues corresponding to the first Kaluza–Klein excitation of the τ-field.
The simulation (v6) demonstrates robust energy splitting (ΔE ≈ 0.8 TeV) induced by an effective interaction term gintg_{\text{int}}gint, consistent with the phenomenological predictions of the TDF model and within LHC Run 3 reach.
All Python scripts, QPE outputs, and LaTeX sources are included to ensure full reproducibility.
This work bridges quantum algorithm research and high-energy phenomenology, offering a practical quantum-simulation approach to testing extra-dimensional field dynamics.

Code Repository:
https://github.com/bahman2017/tau_delay