Investigation of Automated Design of Quantum Circuits for Imaginary Time Evolution Methods Using Deep Reinforcement Learning

Efficient ground state search is fundamental to advancing combinatorial optimization problems and quantum chemistry. While the Variational Imaginary Time Evolution (VITE) method offers a useful alternative to Variational Quantum Eigensolver (VQE), and Quantum Approximate Optimization Algorithm (QAOA), its implementation on Noisy Intermediate-Scale Quantum (NISQ) devices is severely limited by the gate counts and depth of manually designed ansatz. Here, we present an automated framework for VITE circuit design using Double Deep-Q Networks (DDQN). Our approach treats circuit construction as a multi-objective optimization problem, simultaneously minimizing energy expectation values and optimizing circuit complexity. By introducing adoptive thresholds, we demonstrate significant hardware overhead reductions. In Max-Cut problems, our agent autonomously discovered circuits with approximately 37\% fewer gates and 43\% less depth than standard hardware-efficient ansatz on average. For molecular hydrogen ($H_2$), the DDQN also achieved the Full-CI limit, with maintaining a significantly shallower circuit. These results suggest that deep reinforcement learning can be helpful to find non-intuitive, optimal circuit structures, providing a pathway toward efficient, hardware-aware quantum algorithm design.