- Equations of CFD are inherently non-linear - Solved using an outer linearization step and an inner solution of a linear system of equations - The standard algorithm for solving a linear system of equations is the Harrow, Hassidim, Lloyd (HHL) algorithm which requires a fault tolerant machine - [[Riverlane]] and [[Universal Quantum]] have error corrected quantum computing and scalable design #### Value of better CFD **Hermitian Matrices** Hermitian matrices can be understood as the complex extension of real symmetric matrices. typically means the complex conjugate only, and not the conjugate **transpose**. ![[Pasted image 20210209180243.png]] **Poisson's equation** is an [elliptic partial differential equation](https://en.wikipedia.org/wiki/Elliptic_partial_differential_equation "Elliptic partial differential equation") of broad utility in [theoretical physics](https://en.wikipedia.org/wiki/Theoretical_physics "Theoretical physics"). - For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field. - It is a generalization of [Laplace's equation](https://en.wikipedia.org/wiki/Laplace%27s_equation "Laplace's equation"), which is also frequently seen in physics. [[Lattice Boltzman Models]]