This study, co-authored by researchers from Bio2Q and Keio University, presents the first quantum algorithm specifically designed for metabolic network analysis, introducing a quantum computing framework for flux balance analysis (FBA) to model cellular metabolism. FBA is widely used to predict how metabolic pathways allocate reaction fluxes to maximize biological objectives such as biomass production or energy generation. However, extending these analyses to increasingly large, dynamic, or multi-species metabolic networks becomes exceedingly computationally complex because solving the underlying optimization problem requires repeated large-scale matrix inversions. To address this bottleneck, these researchers developed a quantum interior point method (QIPM) that reformulates the FBA optimization problem for execution on a fault-tolerant quantum computer using quantum singular value transformation (QSVT), a quantum algorithm for efficiently solving linear systems. Recognizing that QSVT performance is strongly limited by the condition number of the optimization matrices, they introduced a novel null-space projection and adaptive regularization strategy that dramatically improves numerical stability by reducing the condition number before quantum matrix inversion. The framework was validated through numerical simulations of the glycolysis and tricarboxylic acid (TCA) cycle metabolic network, where the quantum algorithm accurately converged to the classical optimal solution, while successfully reproducing biologically meaningful flux distributions. Although current quantum hardware is not yet capable of providing practical speedups for these problems, this study establishes the first quantum algorithm tailored to metabolic pathway analysis and provides a scalable foundation for future applications to genome-scale metabolism, dynamic flux balance analysis, microbiome modeling, and other complex biological systems that may eventually exceed the capabilities of classical computational methods.