What question did this study set out to answer?

The aim is to investigate quantum temporal reversal learning and its performance in trapped-ion quantum processing units (QPU).

April 21, 2026Open Access

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

Key Points

The aim is to investigate quantum temporal reversal learning and its performance in trapped-ion quantum processing units (QPU).
Applied quantum temporal reversal learning (QTRLS) to minimize ground state energy of H₂ in simulations and trials.
Conducted multiple trials on an 8-qubit trapped-ion QPU and evaluated forward-reverse coupling fidelity (F_R).
Confirmed convergence through extensive testing across various qubit scales and compared results against simulated data.
Achieved 20/20 convergence in H₂ ground state energy minimization with a mean final energy of −1.8478 Hartree.
Measurable F_R coupling at 8-qubit scale confirmed, with mean F_R = 0.8538 ± 0.0099 across trials.
All tested configurations validated a full scaling law with 100% convergence rates across 4, 8, and 16 qubits.

Abstract

v10 (20 April 2026): Added VQE H₂ simulator results (qtrlsᵥqeₕ2ᵣesults. 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. FR coupling confirmed. v9 (18 April 2026): Added 8-qubit multi-trial hardware validation results. 5 independent trials on IonQ Forte QPU. Mean FR = 0. 8538 ± 0. 0099, range 0. 8360, 0. 8642. Confirms reproducibility of FR signal at 8-qubit scale. Single-trial reference FR = 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, FR = 0. 8618 Trial 2: fwd 3b93178a-3b07-11f1-bd96-96a58bb47abc, rev 3cbc3722-3b07-11f1-bd96-96a58bb47abc, FR = 0. 8539 Trial 3: fwd 966aad70-3b08-11f1-bd96-96a58bb47abc, rev 97d35658-3b08-11f1-bd96-96a58bb47abc, FR = 0. 8529 Trial 4: fwd 81bd4198-3b09-11f1-bd96-96a58bb47abc, rev 83143c90-3b09-11f1-bd96-96a58bb47abc, FR = 0. 8360 Trial 5: fwd 6e5128e4-3b0a-11f1-bd96-96a58bb47abc, rev 6f92a930-3b0a-11f1-bd96-96a58bb47abc, FR = 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 FR measurement on IonQ Forte QPU (ionq. qpu. forte-1) via Azure Quantum. 1000 shots each. FR estimated via Bhattacharyya coefficient between forward and reverse measurement distributions. Hardware FR = 0. 8671 vs simulator baseline mean of 0. 9179 (50 trials). Confirms FR 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 FR = 0. 9945 (single trial), 0. 9949 ± 0. 0016 (5-trial mean). Simulator baseline mean FR = 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: qtrlsₕardwareᵣesult. json, qtrlsₕardwareₘultitrials. json, qtrlsₕardware₈q. json, qtrlsₕardware₈qₘultitrialsᵥ2. json, qtrlsᵥqeₕ2ᵣesults. 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 FR = 0. 9508 ± 0. 0080, mean convergence iteration 123. 8 8-qubit: 50/50 convergence, mean final FR = 0. 9179 ± 0. 0022, mean convergence iteration 30. 8 16-qubit: 50/50 convergence, mean final FR = 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 FR = 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 FR = 0. 9945. Job IDs included. v6 — 18 April 2026: 16-qubit scaling validation complete. 50/50 convergence. Mean FR = 0. 7924. 150/150 total trials converged. v5 — 17 April 2026: 8-qubit scaling validation. 50/50 convergence. Mean FR = 0. 9179. Mean convergence iteration 30. 8. v4 — 17 April 2026: 50-trial 4-qubit independent validation. 100% convergence. Mean FR = 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 FR 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.

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

Key Points

Abstract

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