This workshop introduces the primary mathematical formalisms and algorithmic primitives utilized in the quantum simulation of differential equations. The lectures will discuss the underlying quantum subroutines such as Hamiltonian simulation and quantum linear systems algorithms, and modern tools for quantum algorithms design based on quantum signal processing and quantum singular value transformation. Following the linear theory, the workshop will pivot to the significantly more complex domain of nonlinear differential equations. The intrinsic mathematical challenges that nonlinear dynamics pose to quantum computing will be discussed and existing theoretical frameworks for mapping nonlinear systems to quantum amenable linear forms are introduced.

Target Audience: This workshop is designed for participants with familiarity with the core concepts of quantum computing. While the workshop is instructional, it assumes a basic knowledge of quantum circuits and quantum algorithms.