Quantum computing of reacting flows via Hamiltonian simulation

TL;DR

This paper introduces quantum algorithms for simulating reacting flows by transforming the governing equations into a Hamiltonian form, achieving exponential speedups over classical methods, and validating them on quantum simulators.

Contribution

It develops quantum spectral and finite difference methods for reacting flows, enabling one-shot solutions with exponential acceleration and validation on quantum simulators.

Findings

Quantum spectral method shows exponential speedup over classical methods.

Quantum finite difference method achieves exponential speedup in high dimensions.

Quantum algorithms accurately simulate convection, diffusion, and reaction processes.

Abstract

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.