Carleman Linearization Application for Chemical Reaction and Reacting Flow Toward Quantum Computing
Abstract
Reacting flows are governed by the conservation equations of mass, momentum, energy, and chemical species, and exhibit strong nonlinearity due to convection and chemical reactions. As quantum computers are inherently limited to linear operations, a bridging method is required to enable their application to such nonlinear systems. This study proposes an approach using the Carleman linearization to integrate quantum computing into reacting flow analysis, with a focus on the nonlinear temperature dependence described by the Arrhenius equation. To handle the exponential form of the reaction rate, a Taylor series expansion is employed. The present method is validated through numerical simulations of fuel ignition. The impacts of the truncation order in the Carleman linearization and the polynomial order in the Taylor expansion are systematically examined. The results demonstrate that higher-order approximations enhance the accuracy but may also introduce numerical stiffness. Overall, the findings confirm the validity and potential of the proposed framework for quantum-assisted reacting flow computations.
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