Abstract
Quantum systems in near-term devices operate in noisy, open-system regimes where decoherence and control
imperfections are unavoidable. This study presents a physics-informed neural-network framework for modelling, noiseaware simulation, and residual-based control of open quantum systems, validated against a closed-form Lindblad solution
for a driven, amplitude-damped qubit rather than a numerical reference. Across three random seeds, the trained network
reproduces population and coherence dynamics with a mean RMSE of 0.00060 and a standard deviation of 0.00054. The
mixed-state fidelity exceeds 0.999999 over the evaluation trajectory, while the squared Bloch-vector norm remains within
the physical bound for the main modelling benchmark. Removing the Fourier-feature input encoding produces a 70-fold
degradation in RMSE, confirming a strong representational benefit for the oscillatory dynamics. Direct comparison against
fourth-order Runge-Kutta integration shows the classical solver to be approximately five orders of magnitude faster and
two orders more accurate at this scale; the value of the proposed framework for a single qubit therefore lies in data-free,
physics-constrained modelling rather than computational speed. A residual-based state-transfer control demonstration and
a control-effort sweep further reveal a clear fidelity-versus-energy trade-off and a marked reduction in seed-to-seed
variation as regularisation increases. These results support physics-constrained learning as a faithful approach to singlequbit open-system modelling and control, while motivating further validation on multi-qubit systems before broader
scalability claims are made.