GSQAS: Graph Self-supervised Quantum Architecture Search

Quantum Architecture Search (QAS) is a promising approach for designing quantum circuits specifically tailored for variational quantum algorithms (VQAs). However, existing QAS algorithms require calculating the ground-truth performances of a substantial number of quantum circuits during the search process, rendering them computationally demanding and limiting their applicability to large-scale quantum circuits. Recently, a predictor-based QAS has been proposed to address this challenge by estimating circuit performance directly based on their structures using a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is highly time-consuming to obtain a substantial number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS that trains a predictor by self-supervised learning. Specifically, we first pre-train a graph encoder using a well-designed pretext task on a large number of unlabeled quantum circuits, aiming to generate meaningful representations of quantum circuits. Subsequently, the downstream predictor is trained on a small set of quantum circuits' representations and their corresponding labels. Once the encoder is trained, it becomes applicable to various downstream tasks. To effectively encode spatial topology information and avoid huge dimensions of feature vectors for large-scale quantum circuits, we propose a graph-based encoding scheme for quantum circuits. Simulation results on QAS for variational quantum eigensolver and quantum state classification demonstrate that GSQAS outperforms the state-of-the-art predictor-based QAS, yielding superior performance with fewer labeled circuits.