Quantum algorithm for metabolic network analysis

Abstract Biological systems, such as cellular metabolism, involve thousands of reactions that together determine how cells grow, respond to their environment, and produce energy. Modeling and analyzing these systems require solving very large mathematical problems that can quickly become computationally prohibitive. To address this challenge, we present a quantum algorithm to analyze metabolic networks, focusing on flux balance analysis as a representative case. We use a quantum interior point method consisting of a quantum subroutine for matrix inversion. Specifically, we reformulate the metabolic optimization problem for efficient execution on a quantum computer using quantum singular value transformation, enabling a rapid solution of complex systems that arise in flux balance analysis. This quantum approach offers a potential computational advantage over classical interior point methods for large and well-conditioned networks. We demonstrate the practical applicability of our method with numerical simulations on the glycolysis and tricarboxylic acid (TCA) cycle network and show that the quantum solution converges to the correct biological objective. This work represents the first application of quantum algorithms to metabolic pathway analysis, establishing a new direction for quantum computational biology and paving the way for quantum approaches to large-scale biological optimization.