The advent of noisy intermediate-scale quantum (NISQ) devices provide crucial promise for the development of quantum algorithms. Variational quantum algorithms have emerged as one of the best hopes to utilize NISQ devices. Among these is the famous variational quantum eigensolver (VQE), where one trains a parameterized and fixed quantum circuit (or an ansatz) to accomplish the task. However, VQE also suffers from some serious challenges, which are training difficulty and accuracy reduction due to deep quantum circuit and hardware noise. Motivated by these issues, we propose a runtime and resource-efficient scheme, Monto Carlo tree (MCT) search-based quantum circuit architecture optimization, where the ansatz is built in the variable form. Our approach first models the search space with a MCT and regards it as a supernet, where we make use of layers dependence to reduce the size of the search space. Second, a two-stage scheme is proposed for the search space training, where weight sharing and warm-up strategies are employed to avoid huge computation cost. Training results are stored in nodes of the MCT for future decisions, and hierarchical node selection is presented to obtain an optimal ansatz. As a proof of principle, we carry out a series of numerical experiments for condensed matter and quantum chemistry in a quantum simulator with and without noise. Consequently, our scheme can be efficient to mitigate trainability and accuracy issues by minimizing the ansatz depth and the number of entanglement gates.
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