A Unitary Algorithm for Solving the Advection Equation

WILLIAM GREGORY, YUAN SHI, University of Colorado at Boulder, — The advection equation has a large number of applications in the field of fluid dynamics, an important topic for a large variety of subjects including aeronautics, meteorology, and plasma physics. A quantum algorithm for the advection equation could solve high-dimensional advection problems. A unitary algorithm for this equation is a crucial step for building a quantum algorithm. I present multiple unitary solutions to the advection equation assuming different boundary conditions and handling a variety of functions.The results obtained thus far show that we have developed a working algorithm to decompose into pauli matrices which can then be represented by a series of quantum gates used to build a quantum circuit that run on quantum hardware.