  The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected
to accelerate solving large-scale linear ordinary differential equations
(ODEs). To apply the HHL to non-linear problems such as chemical reactions, the
system must be linearized. In this study, Carleman linearization was utilized
to transform nonlinear first-order ODEs of chemical reactions into linear ODEs.
Although this linearization theoretically requires the generation of an
infinite matrix, the original nonlinear equations can be reconstructed. For the
practical use, the linearized system should be truncated with finite size and
analysis precision can be determined by the extent of the truncation. Matrix
should be sufficiently large so that the precision is satisfied because quantum
computers can treat. Our method was applied to a one-variable nonlinear dy/dt =
-y^2 system to investigate the effect of truncation orders in Carleman
linearization and time step size on the absolute error. Subsequently, two
zero-dimensional homogeneous ignition problems for H2/air and CH4/air gas
mixtures were solved. The results revealed that the proposed method could
accurately reproduce reference data. Furthermore, an increase in the truncation
order in Carleman linearization improved accuracy even with a large time-step
size. Thus, our approach can provide accurate numerical simulations rapidly for
complex combustion systems.
