Adaptive Quantum Control and Compression Diagnostics Using the DVR Framework

Addressing the dual challenges of decoherence and data overhead in practical quantum systems, we introduce a novel Difference-based Variational Reconstruction (DVR) framework for adaptive quantum control and efficient signal compression. Through numerical experiments, we demonstrate that DVR enables high-fidelity quantum control even under strong decoherence, achieving final fidelities exceeding 0.93 across a range of damping strengths ($\gamma = 0.5$, $0.8$, $1.2$), while maintaining purity close to 1. Simultaneously, DVR compresses observable trajectories by exploiting their intrinsic difference-based structure, providing scalable low-rank approximations that significantly reduce storage and computational complexity. Our results show that DVR forms a unified formalism for both real-time control and offline analysis of quantum dynamics, paving the way for resource-efficient quantum experiments and robust device characterization.