Challenges for quantum computation of nonlinear dynamical systems using linear representations

Understand

A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space.

• Linear representations, such as the Koopman representation and Koopman von Neumann mechanics, have regained attention from the dynamical-systems research community.
• Here, we aim to present a unified theoretical framework, currently missing in the literature, with which one can compare and relate existing methods, their conceptual basis, and their representations.
• We also aim to show that, despite the fact that quantum simulation of nonlinear classical systems may be possible with such linear representations, a necessary projection into a feasible finite-dimensional space will in practice eventually induce numerical artifacts which can be hard to eliminate or even control.