This post was contributed by Jiaqi Leng, Joseph Li, Xiaodi Wu
Scientists and engineers face numerous computational challenges in fields like fluid dynamics [1], modeling heat and sound propagation [2], and aircraft design [3]. Simulating partial differential equations (PDEs) in high dimensions offers a powerful approach to addressing these challenges. However, solving these high-dimensional differential equations is challenging for classical computers, as the computational complexity increases exponentially with the problem dimension. Quantum computers, capable of efficiently manipulating high-dimensional data in a non-classical way, offer potential for addressing these complex problems. Over the past decades, there has been progress in developing quantum algorithms for PDEs, including both linear and nonlinear equations [4,5,6]. However, most existing quantum algorithms rely on sophisticated input models of the problem data, such as block-encoded matrices and…
