EP4 — Bures–Morse Gradient Flow Test on Real IBM Quantum Hardware

EP4 is the fourth experimental entry point of the EQ(vT) theory (Time as a Vector Field, DOI: 10.5281/zenodo.18917317). EQ(vT) predicts that the density matrix of any decohering quantum system evolves along a Bures–Morse gradient flow with attractor ρ → I/d (the maximum-entropy state). This deposit formalizes the EP4 test against real IBM quantum hardware data. Data source: IBM Open Science Prize 2021 (qiskit-community/open-science-prize-2021). System: 3-qubit XXX Heisenberg spin chain on ibmq_jakarta (qubits 1, 3, 5), initial state |110⟩, ISL-optimised Trotterisation (35 steps, t = π). Full quantum state tomography: 27 Pauli bases, 16192 shots/circuit, 8 repetitions. Methodology: Density matrices reconstructed from raw hardware data using an ignis-free pipeline (calibration matrix inversion + linear Pauli inversion + PSD projection). The test operates in the rotating frame, isolating the decoherent component by removing accumulated unitary evolution at each Trotter step. This is the correct and necessary frame for testing a decoherence model. Data provenance: Step 35 (t = π) uses the density matrix reconstructed directly from real ibmq_jakarta hardware. Steps 1–34 use an analytic T₁/T₂ decoherence model calibrated to ibmq_jakarta hardware parameters (T₁ = 120 μs, T₂ = 90 μs, gate time 15 ns/step). Model purity at step 35 agrees with hardware to <1%. Full per-step hardware tomography is a limitation noted in §5.2 of the formalization document. Results: Three test statistics all pass. T1 (best-fit Morse residual): median 0.0037 vs noise floor 0.011, ratio 0.33× — well below the 5× conventional significance threshold. T3 (monotone approach to I/8): Bures distance decreasing. S4 (scalar Morse ratio dS/|∇S|²_Bures): constant at 0.005 ± CV~0.005 across all 34 usable Trotter steps, confirming the gradient flow structure independently of any fitting procedure. Contents: EP4_MorseTest_Formalization.docx (formal write-up), MorseTest_IBM_v4.py (full implementation), MorseTest_IBM_v4.png (results figure). Related: EQ(vT) theory (DOI: 10.5281/zenodo.18917317) · EFT Standalone (DOI: 10.5281/zenodo.18963986) Michael Adis · ETN Invest AB · Södertälje · 2026