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

arXiv: https://arxiv.org/abs/2601.06392 · HTML: https://mlsanity.com/paper/2601.06392/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 10 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [On the Inductive Bias of Neural Tangent Kernels](https://mlsanity.com/paper/1905.12173/) (2019)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [On Quadratic Penalties in Elastic Weight Consolidation](https://mlsanity.com/paper/1712.03847/) (2017)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression](https://mlsanity.com/paper/2206.04804/) (2022)
- [Federated Quantum Natural Gradient Descent for Quantum Federated Learning](https://mlsanity.com/paper/2209.00564/) (2022)
- [TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computing](https://mlsanity.com/paper/2508.01116/) (2025)

## Abstract (arXiv)

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.