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. As a result a practical, reliable and accurate way to use quantum computation for solving general nonlinear dynamical systems is still an open problem.

翻译：最近的一些研究认为,线性表示法对于用量子计算机解决非线性动态系统是合适的,这些计算机从根本上在希尔伯特空间的波函数上线性地运行。 科普曼代表和科普曼冯纽曼机械等线性表示法已经重新引起动态系统研究界的注意。 这里,我们的目标是提出一个统一理论框架,在文献中目前缺少这个框架,可以比较和联系现有方法、其概念基础及其表述法。 我们还旨在表明,尽管非线性古典系统的数量模拟可能随着这种线性表示法的出现而成为可能,但对可行的有限空间的必要预测实际上最终将引出难以消除或甚至难以控制的数字文物。 因此,使用量性计算法解决一般非线性动态系统的实际、可靠和准确方式仍然是一个尚未解决的问题。