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

TL;DR

This paper introduces a novel dimensionality reduction method using the Jacobi-Davidson algorithm, enabling efficient quantum dynamics computations in linear time relative to the Hilbert space size.

Contribution

It presents a new application of the Jacobi-Davidson algorithm combined with matrix-free methods for efficient quantum state dynamics simulation.

Findings

Achieves $ ext{O}(n)$ computational complexity for quantum dynamics

Utilizes matrix-free implementations for efficiency

Demonstrates effectiveness in high-dimensional quantum systems

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.