Tractable $\textit{a}$ $\textit{priori}$ Dimensionality Reduction for Quantum Dynamics

Abstract

In this short letter, I present a powerful application in dimensionality reduction of the lesser-used Jacobi-Davidson algorithm for the generalized eigenvalue decomposition. When combined with matrix-free implementations of relevant operators, this technique allows for the computation of the dynamics of an arbitrary quantum state to be done in $\mathcal{O}(n)$ time, where $n$ is the size of the original Hilbert space.