  Variational quantum algorithms (VQAs) have been successfully applied to
quantum approximate optimization algorithms, variational quantum compiling and
quantum machine learning models. The performances of VQAs largely depend on the
architecture of parameterized quantum circuits (PQCs). Quantum architecture
search (QAS) aims to automate the design of PQCs in different VQAs with
classical optimization algorithms. However, current QAS algorithms do not use
prior experiences and search the quantum architecture from scratch for each new
task, which is inefficient and time consuming. In this paper, we propose a meta
quantum architecture search (MetaQAS) algorithm, which learns good
initialization heuristics of the architecture (i.e., meta-architecture), along
with the meta-parameters of quantum gates from a number of training tasks such
that they can adapt to new tasks with a small number of gradient updates, which
leads to fast learning on new tasks. The proposed MetaQAS can be used with
arbitrary gradient-based QAS algorithms. Simulation results of variational
quantum compiling on three- and four-qubit circuits show that the architectures
optimized by MetaQAS converge much faster than a state-of-the-art
gradient-based QAS algorithm, namely DQAS. MetaQAS also achieves a better
solution than DQAS after fine-tuning of gate parameters.
