Quantum computing is expected to accelerate large–scale numerical simulations, while inverse matrix computation remains a critical bottleneck due to the strong dependence of quantum circuit complexity on the matrix condition number [1]. Since inverse problems are ubiquitous in Computer-Aided Engineering (CAE), mitigating this condition-number dependence is essential for practical quantum acceleration of computational mechanics. In this study, we propose a Quantum Gradient Flow Algorithm (QGFA) for inverse matrix computation focusing on symmetric positive definite operators arising in numerical simulations [2]. Instead of directly applying matrix inversion, the proposed approach reformulates the inverse problem as a stable continuous-time relaxation process associated with energy minimization, and utilizes its finite-time evolution to approximate the inverse action. By exploiting the monotonic convergence property guaranteed by positive definiteness, the proposed method enables an efficient approximation of inverse operations without explicitly resolving ill-conditioned spectra. Numerical examples of finite element analyses demonstrate that the quantum circuit size required for inverse computations can be significantly reduced compared to conventional quantum linear solvers, especially for large condition numbers.