Quantum computing of nonlinear reacting flows via the probability density function method

TL;DR

This paper introduces a quantum computing framework for nonlinear reacting flows using a probability density function approach, transforming the problem into a high-dimensional linear system and developing efficient measurement algorithms to extract physical quantities.

Contribution

It presents a novel quantum algorithm that solves nonlinear reacting flow equations via linearization and efficient measurement, enabling quantum advantage in complex fluid simulations.

Findings

Validated measurement algorithm on beta distributions

Demonstrated PDF evolution in a stirred reactor

Achieved polynomial complexity in measurement process

Abstract

Quantum computing offers the promise of speedups for scientific computations, but its application to reacting flows is hindered by nonlinear source terms, the challenges of time-dependent simulations, and the difficulty of extracting meaningful physical quantities from quantum states. We employ a probability density function (PDF) formulation to transform the nonlinear reacting-flow governing equations into high-dimensional linear ones. The entire temporal evolution is then solved as a single large linear system using the history state method, which avoids the measurement bottleneck of conventional time-marching schemes and fully leverages the advantages of quantum linear system algorithms. To extract the quantity of interest from the resulting quantum state, we develop an efficient algorithm to measure the statistical moments of the PDF, bypassing the need for costly full-state tomography. A computational complexity analysis shows that the measurement algorithm achieves a complexity polynomial in the logarithm of the system size using low-order polynomial approximations, compared to the exponential cost of the exact operator, thereby retaining the quantum advantage gained from solving the linear system. We validate the framework in two stages: an a priori test confirms the accuracy of the measurement algorithm on beta distributions with known analytical moments, and a perfectly stirred reactor simulation demonstrates the capability to capture the PDF evolution and statistics of a nonlinear reactive system. This work establishes a pathway for applying quantum computing to nonlinear reacting flows.