Quantum Temporal Reversal Learning System (QTRLS): A Universal Algorithm for Reversible Quantum Optimisation and Thermodynamic Energy Recovery via Time-Reversal Protocols

Hardware Validation (18 April 2026) Following simulator validation across 150 trials (4, 8, and 16 qubit scales), QTRLS v3 was validated on real quantum hardware via IonQ Forte QPU (ionq. qpu. forte-1) accessed through Azure Quantum. A 4-qubit FR measurement was performed using the native IonQ JSON circuit format, submitting forward and reversed QTRLS circuits (theta = 0. 5, 1. 2, 0. 8, 1. 7, thetaₒpt = 1. 1, 0. 9, 1. 4, 0. 6, 1000 shots each). FR was computed as the Bhattacharyya coefficient between the forward and reversed measurement distributions — a hardware-compatible proxy for the statevector fidelity used in simulation. Hardware result: FR = 0. 9945 This compares to the 4-qubit simulator baseline mean of FR = 0. 9508 across 50 trials. The high hardware FR reflects IonQ Forte's gate fidelity at this circuit depth (32 gates forward, 60 gates reversed), confirming that the FR coupling signal is measurable on physical quantum hardware. Verifiable job provenance: Forward job ID: 5c4dc0da-3ac9-11f1-a37c-96a58bb47abc Reversed 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 are included in qtrlsₕardwareᵣesult. json. Version 6 — 18 April 2026: 16-qubit scaling validation complete. 50/50 convergence. Mean final FR 0. 7924. Full scalinglaw confirmed across 4, 8, and 16 qubits. 150/150 totaltrials converged. Code on request. Patent GB2608473. 1. Version 5 — 17 April 2026: 8-qubit scaling validation. 50/50 convergence with smart initialization. Mean convergence iteration 30. 8. Mean final FR 0. 9179. Full comparison: 4-qubit (50/50, iter 123. 8, FR 0. 9508) vs 8-qubit smart init (50/50, iter 30. 8, FR 0. 9179). Code available on request. Patent pending GB2608473. 1. Version 4 UPDATE — 17 April 2026: 50-trial independent validation. 100% convergence rate. Mean final FR 0. 9508. Code available on request. Patent pending GB2608473. 1. Version 3. 1 UPDATE — 17 April 2026: Implementation details removed from correction notice for confidentiality. Full technical details in forthcoming paper. Results unchanged from v3. Version 3 UPDATE — 17 April 2026: Critical implementation error in v2 corrected. Real quantum gradients implemented. See qtrlsᵦenodoᵥ3. md for full correction notice. Code available upon request. Version 2 (17 April 2026): First simulation validation results added. 50 independent runs demonstrate 100% pass rate above FR > 0. 85 (mean FR = 0. 942). 60-iteration convergence demonstration achieves 80. 7% loss reduction converging at iteration 54. First experimental observation of the convergence-fidelity trade-off reported. Simulation code (qtrls₄qubit. py, qtrlsconvergence. py) included as supplementary files.