  We report the quantum computing of reacting flows by simulating the
Hamiltonian dynamics. The scalar transport equation for reacting flows is
transformed into a Hamiltonian system, mapping the dissipative and
non-Hermitian problem in physical space to a Hermitian one in a
higher-dimensional space. Using this approach, we develop the quantum spectral
and finite difference methods for simulating reacting flows in periodic and
general conditions, respectively. The present quantum computing algorithms
offer a ``one-shot'' solution for a given time without temporal discretization,
avoiding iterative quantum state preparation and measurement. We compare
computational complexities of the quantum and classical algorithms. The quantum
spectral method exhibits exponential acceleration relative to its classical
counterpart, and the quantum finite difference method can achieve exponential
speedup in high-dimensional problems. The quantum algorithms are validated on
quantum computing simulators with the Qiskit package. The validation cases
cover one- and two-dimensional reacting flows with a linear source term and
periodic or inlet-outlet boundary conditions. The results obtained from the
quantum spectral and finite difference methods agree with analytical and
classical simulation results. They accurately capture the convection,
diffusion, and reaction processes. This demonstrates the potential of quantum
computing as an efficient tool for the simulation of reactive flows in
combustion.
