Quantum Temporal Reversal Learning: Forward-Reverse Circuit Fidelity as an Adaptive Learning Rate Signal with Hardware Validation on Trapped-Ion QPU

v10 (20 April 2026): Added VQE H₂ simulator results (qtrls_vqe_h2_results.json). QTRLS applied to H₂ ground state energy minimisation (STO-3G basis, 4 qubits). 20/20 trials converged. Mean final energy −1.8478 Hartree against exact −1.8572 Hartree. F_R coupling confirmed. v9 (18 April 2026): Added 8-qubit multi-trial hardware validation results. 5 independent trials on IonQ Forte QPU. Mean F_R = 0.8538 ± 0.0099, range [0.8360, 0.8642]. Confirms reproducibility of F_R signal at 8-qubit scale. Single-trial reference F_R = 0.8671 is within one standard deviation of multi-trial mean. Trial job IDs: Trial 1: fwd 966fa5b2-3b05-11f1-bd96-96a58bb47abc, rev 985cf99c-3b05-11f1-bd96-96a58bb47abc, F_R = 0.8618 Trial 2: fwd 3b93178a-3b07-11f1-bd96-96a58bb47abc, rev 3cbc3722-3b07-11f1-bd96-96a58bb47abc, F_R = 0.8539 Trial 3: fwd 966aad70-3b08-11f1-bd96-96a58bb47abc, rev 97d35658-3b08-11f1-bd96-96a58bb47abc, F_R = 0.8529 Trial 4: fwd 81bd4198-3b09-11f1-bd96-96a58bb47abc, rev 83143c90-3b09-11f1-bd96-96a58bb47abc, F_R = 0.8360 Trial 5: fwd 6e5128e4-3b0a-11f1-bd96-96a58bb47abc, rev 6f92a930-3b0a-11f1-bd96-96a58bb47abc, F_R = 0.8642 v8 (18 April 2026): Added 8-qubit hardware validation results. Paper submitted to npj Quantum Information on 18 April 2026 (submission ID: 253a94b1-2733-475e-a1f1-16c06d506b40). 8-Qubit Hardware Validation (18 April 2026) Single-trial 8-qubit F_R measurement on IonQ Forte QPU (ionq.qpu.forte-1) via Azure Quantum. 1000 shots each. F_R estimated via Bhattacharyya coefficient between forward and reverse measurement distributions. Hardware F_R = 0.8671 vs simulator baseline mean of 0.9179 (50 trials). Confirms F_R coupling is measurable at 8-qubit scale on real hardware. Verifiable job provenance: Forward job ID: 4d81dfb8-3ade-11f1-9c84-96a58bb47abc Reverse job ID: 4ec4764c-3ade-11f1-9c84-96a58bb47abc Target: ionq.qpu.forte-1 Workspace: sharaf-hw4 (Azure Quantum, East US) Date: 18 April 2026 4-Qubit Hardware Validation (18 April 2026) Single-trial and 5-trial validation on IonQ Forte QPU via Azure Quantum. 1000 shots each. Hardware F_R = 0.9945 (single trial), 0.9949 ± 0.0016 (5-trial mean). Simulator baseline mean F_R = 0.9508 (50 trials). Verifiable job provenance: Forward job ID: 5c4dc0da-3ac9-11f1-a37c-96a58bb47abc Reverse job ID: 5d6bb990-3ac9-11f1-a37c-96a58bb47abc Target: ionq.qpu.forte-1 Workspace: sharaf-hw4 (Azure Quantum, East US) Date: 18 April 2026 Raw results: qtrls_hardware_result.json, qtrls_hardware_multitrials.json, qtrls_hardware_8q.json, qtrls_hardware_8q_multitrials_v2.json, qtrls_vqe_h2_results.json Simulator Validation (17–18 April 2026) 150/150 trials converged across 4, 8, and 16 qubit scales. All gradients computed via parameter shift rule on real quantum circuits (v3 correction, 17 April 2026). 4-qubit: 50/50 convergence, mean final F_R = 0.9508 ± 0.0080, mean convergence iteration 123.8 8-qubit: 50/50 convergence, mean final F_R = 0.9179 ± 0.0022, mean convergence iteration 30.8 16-qubit: 50/50 convergence, mean final F_R = 0.7924 ± 0.0143, mean convergence iteration 37.8 Full scaling law confirmed across all three qubit scales. Version History v10 — 20 April 2026: VQE H₂ simulator results added. 20/20 convergence. Mean final energy −1.8478 Hartree. v9 — 18 April 2026: 8-qubit multi-trial hardware results added. 5 trials, mean F_R = 0.8538 ± 0.0099. v8 — 18 April 2026: 8-qubit single-trial hardware results added. Paper submitted to npj Quantum Information. v7 — 18 April 2026: 4-qubit hardware validation on IonQ Forte. Single-trial F_R = 0.9945. Job IDs included. v6 — 18 April 2026: 16-qubit scaling validation complete. 50/50 convergence. Mean F_R = 0.7924. 150/150 total trials converged. v5 — 17 April 2026: 8-qubit scaling validation. 50/50 convergence. Mean F_R = 0.9179. Mean convergence iteration 30.8. v4 — 17 April 2026: 50-trial 4-qubit independent validation. 100% convergence. Mean F_R = 0.9508. v3.1 — 17 April 2026: Implementation details removed from correction notice for confidentiality. v3 — 17 April 2026: Critical implementation error in v2 corrected. All results from v3 onward are valid. v2 — 17 April 2026: First simulation validation results. 50 independent runs, 100% convergence above F_R 0.85. v1 — 13 April 2026: Initial deposit. Patent GB2608473.1 filed. Code available on request. Patent GB2608473.1 (filed 13 April 2026). All hardware results are publicly verifiable via Azure Quantum job IDs.