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

TL;DR

This work tackles two main bottlenecks in quantum machine learning: the prohibitive cost of amplitude encoding for high-dimensional data and catastrophic forgetting during continual learning. It introduces CL-QAS, a framework that fuses Tensor-Train amplitude encoding, bi-loop quantum architecture search, and Elastic Weight Consolidation to enable scalable, hardware-aware continual quantum learning on near-term devices. The authors provide theoretical bounds on TT fidelity, trainability, generalization, and robustness under quantum noise, and validate the approach through ECG classification and financial time-series forecasting, including hardware demonstrations on IBM's Heron processor. The results show that TT-based compression, architecture adaptation, and continual regularization yield improved accuracy and resilience to noise with shallower circuits, suggesting a practical path toward adaptive quantum signal processing in real-world, non-stationary environments.

Abstract

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.

Figures (1)

• Figure 1: Fundamental architecture of the CL-QAS framework. The framework consists of three integrated modules: (i) a continual learning engine that incorporates EWC and hardware-aware penalties in the outer loop, (ii) a Transformer-based reinforcement learning policy that generates adaptive gate sequences for VQCs, and (iii) a VQC classifier trained via cross-entropy loss in the inner loop. Sequential tasks (such as ECG or financial signals) are pre-processed and encoded into quantum states using TT amplitude encoding. During training, the QNN parameters are optimized with respect to a fixed circuit architecture. At the same time, the policy network is updated using detached rewards, enabling adaptive search over quantum architectures across tasks.

Theorems & Definitions (10)

• Lemma 1: Continual Learning Stability
• Theorem 1: Fidelity Bound
• Theorem 2: Trainability Guarantee of CL-QAS
• Corollary 1: Expressivity-Trainability Trade-off
• Lemma 2: Inner-Loop Generalization
• Lemma 3: Outer-Loop Probably Approximately Correct (PAC)-Bayes Bound
• Theorem 3: Overall Generalization Bound
• Lemma 4: Per-task classifier robustness
• Lemma 5: Policy-term robustness
• Theorem 4: Objective-level robustness