Generative AI can be a powerful tool for supporting the design and implementation of quantum applications, whereas the burden of checking whether generated circuits realize the intended computation increases. In this study, we regard this burden of human understanding, checking, and judgment as “trust cost,” and propose a development methodology that integrates AI and formal verification to reduce it. In the proposed development methodology, the implementation is divided into three components: a target mathematical specification, a quantum circuit, and a correspondence theorem and its proof that prove the agreement between the two. This division separates the specifications and theorem statements checked by humans from the theorem proofs entrusted to mechanical checking. As a concrete development example of this proposal, we describe an implementation for the time evolution of a stochastic particle system and its results.