With the growing interest in quantum programs, ensuring their correctness is a fundamental challenge. Although constraint-solving techniques can overcome some limitations of traditional testing and verification, they have not yet been sufficiently explored in the context of quantum programs. To address this gap, we present QSolver, the first quantum constraint solver. QSolver provides a structured framework for handling five types of quantum constraints and incorporates an automated assertion generation module to verify quantum states. QSolver transforms quantum programs and multi-moment constraints into symbolic representations, and utilizes an SMT solver to obtain quantum states that satisfy these constraints. To validate the correctness of the generated input states, QSolver automatically generates assertion programs corresponding to each constraint. Experimental results show that QSolver efficiently processes commonly used quantum gates and demonstrates good scalability across quantum programs of different sizes.