A GNN-based predictor for quantum architecture search

The performance of the variational quantum algorithm (VQA) highly depends on the structure of the quantum circuit. Quantum architecture search (QAS) algorithm aims to automatically search out high-performance quantum circuits for given VQA tasks. However, current QAS algorithms need to calculate the ground-truth performances of a large number of quantum circuits during the searching process, especially for large-scale quantum circuits, which is very time-consuming. In this paper, we propose a predictor based on a graph neural network (GNN), which can largely reduce the computational complexity of the performance evaluation and accelerate the QAS algorithm. We denote the quantum circuit with a directed acyclic graph (DAG), which can well represent the structural and topological information of the quantum circuit. A GNN-based encoder with an asynchronous message-passing scheme is used to encode discrete circuit structures into continuous feature representations, which mimics the computational routine of a quantum circuit on the quantum data. Simulations on the 6-qubit and 10-qubit variational quantum eigensolver (VQE) show that the proposed predictor can learn the latent relationship between circuit structures and their performances. It effectively filters out poorly performing circuits and samples the most promising quantum circuits for evaluation, which avoids a significant computational cost in the performance evaluation and largely improves the sample efficiency.