Quantum Simulation of a 6 TeV Resonance in the 5D τ-Delay Field Model

Quantum Simulation of a 6 TeV Resonance in the 5D τ-Delay Field Model Bahman Masarrat Independent Researcher [email protected] October 28, 2025 Abstract We present the first digital quantum simulation of the five-dimensional τ-delay field model proposed in Ref. [1]. Using a two-qubit controlled-phase Hamiltonian on the Qiskit AerSimulator, we model the interaction between a τ-delay excitation and a delay memory register. The simulation reveals (i) a sharp resonance at τ∗= 0.050 with maximum stability, (ii) undamped coherent oscillations in the survival probability for τ= 0.25, and (iii) a direct energy mapping to a ∼6 TeV scalar-like excitation under a compactification scale R−1= 0.6 TeV. These results provide computational validation of the theoretical prediction of quasi-stable high-energy modes emerging from 5D delay dynamics. The complete simulation code is publicly available on GitHub and will be archived with a DOI via Zenodo. 1 Introduction The 5D τ-delay field model [1] proposes a unified framework for particle physics and gravity based on a dynamical time-delay scalar τ(x, χ) in a compact extra dimension. The model predicts: •particle masses from Mellin poles in delay space, •gravitational modifications from spacetime folds, •and a first Kaluza–Klein (KK) excitation at ∼6 TeV. While analytical results are promising, numerical validation of the dynamical stability of these modes has been lacking. Here, we perform a digital quantum simulation using Qiskit to test the coherence and resonance structure of the τ-delay interaction. 2 Effective Hamiltonian The 5D action includes a scalar delay field Φ(X) coupled to a memory register via an Ising-like term: Heff =g τ Z0Z1,(1) where Z0is the τ-delay excitation (“particle” qubit), Z1is the delay memory (phase register), g= 2.5 is the coupling strength, and τ∈[0,1] is the normalized delay phase. The time evolution is discretized into delay steps, each corresponding to propagation by ∆χ= 1/R in the compact dimension. 1 3 Quantum Circuit Design We implement Eq. (1) using a controlled-phase gate: qc.cp(g * tau, 0, 1) # implements exp(i * g * tau * Z0 Z1) The circuit block is repeated Ntimes to simulate evolution along the χ-direction (the compact coordinate). The initial state is |11⟩(maximal coupling), and after each step we measure the survival probability P1(n)≡Pr qubit 0 = 1 after step n, i.e. the probability that the τ-delay fieldexcitationisstillpresent. 4 Results 4.1 Survival Probability Evolution at Fixed τ Figure 1shows the survival probability over 30 delay steps for a fixed delay phase τ= 0.25. The oscillations remain perfectly coherent and essentially undamped, with a repeat period of roughly 3–4 steps. This behavior indicates a quasi-stable bound mode of the delay interaction. Figure 1: Survival probability P(|1⟩0) of the τ-delay excitation over 30 evolution steps at fixed τ= 0.25. The oscillations between ∼0 and ∼1 persist without decay, demonstrating an undamped long-lived mode. The dotted horizontal line marks the ideal limit P= 1. 4.2 Resonance Scan over τ To locate preferred resonant phases, we scan the stability score as a function of τin the interval τ∈[0.05,0.60]. As shown in Fig. 2, we observe a pronounced peak near τ∗= 0.050. 2 Figure 2: Resonance/stability scan versus delay parameter τ. The vertical dashed line indicates the most stable phase τ∗= 0.050. The stability score (y-axis) captures how robustly the excitation persists under repeated delay evolution. The appearance of a unique τ∗suggests that the τ-delay interaction supports a discrete resonant eigenmode. In other words, the delay behaves like a quantized phase defect that pins a preferred state. 4.3 Energy Mapping We now estimate the physical energy of that resonant mode. With a compactification scale R−1= 0.6 TeV, and with resonance observed after ∼10 delay steps, we take one step in χas R−1andwriteEres ≈ 10×R−1≃6 TeV.(2) This matches the predicted first KK-like excitation reported in Ref. [1] and lies in the energy range probed by the LHC. 5 Discussion Two key observations emerge: 1. Long-lived mode at τ= 0.25.The essentially lossless oscillation of the survival probability suggests that the τ-delay field can host quasi-stable excitations that act like massive particles but are protected by delay coherence rather than by a conventional potential well. 2. Sharp resonance at τ∗= 0.050.The stability peak and its mapping to Eres ∼6 TeV support the interpretation of the first KK/delay excitation as a real, detectable state. This makes the τ-delay field testable on two fronts: (i) high-energy colliders (multi-TeV scalar-like resonances), and (ii) precision interferometry / Ramsey-type delay spectroscopy, where one measures coherent phase memory in a coupled two-mode system. Future work: extend to more than two qubits, include realistic noise channels to extract a decay width Γ, and explore analog simulation on trapped ions or Rydberg arrays to see whether the long-lived state survives in non-digital hardware. 3 6 Code Availability All simulation code, data products, and figure-generation scripts will be made public. •GitHub (development): https://github.com/bahman2017/tau_delay To reproduce locally: git clone https://github.com/bahman2017/tau_delay.git cd tau_delay pip install -r requirements.txt python tdf_quantum_simulation.py Acknowledgments This work was performed using the open-source Qiskit framework. The author thanks the xAI team for conceptual discussions on quantum control and stability scanning. References [1] B. Masarrat, “Minimal Parameter Unification via a Causal Five-Dimensional Delay Field,” Zenodo (2025). DOI: 10.5281/zenodo.17460538. A Simulation Code (Excerpt) def delay_block(tau, g): qc = QuantumCircuit(2) # prepare both qubits in |1> qc.x([0, 1]) # apply controlled phase e^{i g tau Z0 Z1} qc.cp(g * tau, 0, 1) return qc 4