Quantum algorithm for the computation of the reactant conversion rate in homogeneous turbulence

The rapid developments that have occurred in quantum computing platforms over the past few years raise important questions about the potential for applications of this new type of technology to fluid dynamics and combustion problems, and the timescales on which such applications might be possible. As a concrete example, here a quantum algorithm is developed and employed for predicting the rate of reactant conversion in the binary reaction of in non-premixed homogeneous turbulence. These relations are obtained by means of a transported probability density function equation. The quantum algorithm is developed to solve this equation and is shown to yield the rate of the reactants' conversion much more efficiently than current classical methods, achieving a quadratic quantum speedup, in line with expectations for speedups arising from quantum metrology techniques more broadly. This provides an important example of a quantum algorithm with a real engineering application, which can build a connection to present work in turbulent combustion modelling and form the basis for further development of quantum computing platforms and their applications to fluid dynamics.