Variational quantum algorithm (VQA) derives advantages from its error resilience and high flexibility in quantum resource requirements, rendering it broadly applicable in the noisy intermediate-scale quantum era. As the performance of VQA highly relies on the structure of the parameterized quantum circuit, it is worthwhile to propose quantum architecture search (QAS) algorithms to automatically search for high-performance circuits. Nevertheless, existing QAS methods are time-consuming, requiring circuit training to assess circuit performance. This study pioneers training-free QAS by utilizing two training-free proxies to rank quantum circuits, in place of the expensive circuit training employed in conventional QAS. Taking into account the precision and computational overhead of the path-based and expressibility-based proxies, we devise a two-stage progressive training-free QAS (TF-QAS). Initially, directed acyclic graphs (DAGs) are employed for circuit representation, and a zero-cost proxy based on the number of paths in the DAG is designed to filter out a substantial portion of unpromising circuits. Subsequently, an expressibility-based proxy, finely reflecting circuit performance, is employed to identify high-performance circuits from the remaining candidates. These proxies evaluate circuit performance without circuit training, resulting in a remarkable reduction in computational cost compared to current training-based QAS methods. Simulations on three VQE tasks demonstrate that TF-QAS achieves a substantial enhancement of sampling efficiency ranging from 5 to 57 times compared to state-of-the-art QAS, while also being 6 to 17 times faster.

Catastrophic forgetting emerges when a neural network’s parameters undergo continuous updates during the sequential training of multiple tasks. The ongoing adaptation, while enhancing the model’s suitability for new tasks, inadvertently leads to a degradation in performance on previously learned tasks. This challenge significantly impedes the sequential learning capabilities essential for the advancement of artificial general intelligence. The phenomenon of catastrophic forgetting also occurs in the field of quantum machine learning, where parametric quantum circuits serve a role analogous to neural networks. In this study, our focus is to explore strategies for mitigating catastrophic forgetting within quantum learning models for quantum data. In this context, we employ a task-based hard attention mechanism, which automatically generates masks for each task to regulate the network’s learning process and resist catastrophic forgetting. To our knowledge, the proposed method is the first one in the field of quantum machine learning to adjust the model structure to prevent catastrophic forgetting. Numerical simulation results demonstrate that our approach preserves the model’s performance on previous tasks without compromising its ability to acquire new knowledge. This effective resistance to catastrophic forgetting marks a significant stride in advancing quantum continual learning.