ASSESSMENT OF THE APPLICABILITY OF QUANTUM COMPUTATION FOR SOLVING THE PROBLEM OF NUMERICAL HYPERSONIC FLOW
Abstract
Quantum computation is a primary candidate to provide new disruptive means to computations for a range of computational problems too complex for conventional supercomputers. Little attention is given to quantum computation of nonlinear continuum systems such as a viscous fluid which too is hard for classical computers. Such fluid is governed by the Navier-Stokes (NS) nonlinear partial differential equations (PDEs) whose solution is essential to aerospace industry, magnetohydrodynamics, and weather prediction to name a few. The alternative to the Navier-Stokes equations, the direct simulation Monte Carlo (DSMC) method has evolved into a primary workhorse to computationally solve the Boltzmann kinetic equation and is routinely being applied to various flow problems of scientific and technological interest including rarefied hypersonic gas flows. It directly simulates the molecular behaviour of gases by decomposing the motion of the particles into two steps—deterministic movement and stochastic collision via Monte Carlo. However, the DSMC method suffers from very high computational costs, especially in the regime near the continuum limit and in three-dimensional flow problems. The stochastic collision process based on conventional pseudo-random number generators such as the linear congruential method and the Mersenne Twister method occupies a significant amount of computing time, approximately 10 to 25 percent of the whole computing time of DSMC. The aim of this AFOSR Grant application is to study quantum computing algorithms and its optimization for solving NS PDEs and DSMC and assessing the applicability of quantum computation and potential speedup for solving the problem of numerical hypersonic flow. The DSMC algorithms combined with a quantum random number generator will be investigated. Recently, PI proposed and demonstrated an optimization procedure named quantum Karnaugh map to facilitate the efficient design of universal quantum algorithms. In this project, efficient quantum algorithms for NS PDEs with quantum Karnaugh map will be studied.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 20, 2023
- Source ID
- FA23862214052
Entities
People
- David B Ahn
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Seoul