  Quantum algorithms based on variational approaches are one of the most
promising methods to construct quantum solutions and have found a myriad of
applications in the last few years. Despite the adaptability and simplicity,
their scalability and the selection of suitable ans\"atzs remain key
challenges. In this work, we report an algorithmic framework based on nested
Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed
bandit (CMAB) model for the automated design of quantum circuits. Through
numerical experiments, we demonstrated our algorithm applied to various kinds
of problems, including the ground energy problem in quantum chemistry, quantum
optimisation on a graph, solving systems of linear equations, and finding
encoding circuit for quantum error detection codes. Compared to the existing
approaches, the results indicate that our circuit design algorithm can explore
larger search spaces and optimise quantum circuits for larger systems, showing
both versatility and scalability.
