Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing

We introduce CL-QAS, a continual quantum architecture search framework that mitigates the challenges of costly amplitude encoding and catastrophic forgetting in variational quantum circuits. The method uses Tensor-Train encoding to efficiently compress high-dimensional stochastic signals into low-rank quantum feature representations. A bi-loop learning strategy separates circuit parameter optimization from architecture exploration, while an Elastic Weight Consolidation regularization ensures stability across sequential tasks. We derive theoretical upper bounds on approximation, generalization, and robustness under quantum noise, demonstrating that CL-QAS achieves controllable expressivity, sample-efficient generalization, and smooth convergence without barren plateaus. Empirical evaluations on electrocardiogram (ECG)-based signal classification and financial time-series forecasting confirm substantial improvements in accuracy, balanced accuracy, F1 score, and reward. CL-QAS maintains strong forward and backward transfer and exhibits bounded degradation under depolarizing and readout noise, highlighting its potential for adaptive, noise-resilient quantum learning on near-term devices.