美国麻省理工学院Engelhardt, Netta团队研究了黑洞和其他混沌系统学习（伪）随机动力学的复杂性。2025年3月20日出版的《高能物理杂志》发表了这项成果。

最近有人提出，由于忽视了高复杂性信息，非酉黑洞蒸发的朴素半经典预测可以在黑洞的基本描述中得到理解。这一猜想的有效性意味着，任何计算复杂度为多项式有界的算法都无法准确重建黑洞动力学。

在这项工作中，研究组证明了这种有界量子算法无法准确预测（伪）随机幺正动力学，即使它们在这种时间演化下可以访问任意一组多项式复杂的可观测值；这表明“学习”（伪）随机酉在计算上很困难。研究组使用通过（伪）随机动力学对黑洞和更一般的混沌系统进行建模的常见简化。他们考虑的量子算法是完全通用的，它们对黑洞时间演化的尝试猜测同样不受约束：它不需要是线性算子，也可以像任意（如解绑）量子通道一样通用。

附：英文原文

Title: The complexity of learning (pseudo)random dynamics of black holes and other chaotic systems

Author: Yang, Lisa, Engelhardt, Netta

Issue&Volume: 2025-03-20

Abstract: It has been recently proposed that the naive semiclassical prediction of non-unitary black hole evaporation can be understood in the fundamental description of the black hole as a consequence of ignorance of high-complexity information. Validity of this conjecture implies that any algorithm which is polynomially bounded in computational complexity cannot accurately reconstruct the black hole dynamics. In this work, we prove that such bounded quantum algorithms cannot accurately predict (pseudo)random unitary dynamics, even if they are given access to an arbitrary set of polynomially complex observables under this time evolution; this shows that “learning” a (pseudo)random unitary is computationally hard. We use the common simplification of modeling black holes and more generally chaotic systems via (pseudo)random dynamics. The quantum algorithms that we consider are completely general, and their attempted guess for the time evolution of black holes is likewise unconstrained: it need not be a linear operator, and may be as general as an arbitrary (e.g. decohering) quantum channel.

DOI: 10.1007/JHEP03(2025)153

Source: https://link.springer.com/article/10.1007/JHEP03(2025)153