Challenges with Implementing Differentiable Quantum Dynamics

Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the eigendecomposition of a matrix. This work is a survey of existing differentiable programming frameworks for these tasks, finding that no framework natively supports our application requirements fully. We therefore demonstrate a need for broader support of complex-valued, differentiable numerical integration in scientific computing libraries. We further demonstrate that the derivatives of our quantum dynamics application can be computed through a combination of differentiable programming frameworks and handcoding.