Transformer-Based Neural Quantum Digital Twins for Many-Body Quantum Simulation and Optimal Annealing Schedule Design

We introduce Transformer-based Neural Quantum Digital Twins (Tx-NQDTs) to simulate full adiabatic dynamics of many-body quantum systems, including ground and low-lying excited states, at low computational cost. Tx-NQDTs employ a graph-informed Transformer neural network trained to predict spectral properties (energy levels and gap locations) needed for annealing schedule design. We integrate these predictions with an adaptive annealing schedule design based on first-order adiabatic perturbation theory (FOAPT), which slows the evolution near predicted small gaps to maintain adiabaticity. Experiments on a D-Wave quantum annealer (N = 10, 15, 20 qubits, 12 control segments) show that Tx-NQDT-informed schedules significantly improve success probabilities despite hardware noise and calibration drift. The optimized schedules achieve success probabilities 2.2-11.7 percentage points higher than the default linear schedule, outperforming the D-Wave baseline in 44 of 60 cases. These results demonstrate a practical, data-driven route to improved quantum annealing performance on real hardware.