Spectral statistics in dissipative quantum chaos: from random matrices to quantum computers

More than four decades of research on chaos in isolated quantum systems have led to the identification of universal signatures---such as level repulsion---that serve as cornerstones in our understanding of complex quantum dynamics. The emerging field of dissipative quantum chaos explores how these properties manifest in open quantum systems, where interactions with the environment play an essential role. Here, I will discuss the theoretical proposal [1] and the first experimental detection [2] of dissipative quantum chaos and integrability by measuring the complex spacing ratios (CSR) of open many-body quantum systems. Employing gradient-based tomography, we retrieved a ``donut-shaped'' CSR distribution for chaotic dissipative circuits, a hallmark of level repulsion in open quantum systems. In integrable circuits, spectral correlations vanish, as evidenced by a sharp peak at the origin. Increasing circuit depth induces an integrability-to-chaos crossover, demonstrating that intrinsic hardware noise is itself a source of dissipative quantum chaos. Our results revealed universal spectral features of dissipative many-body systems and established modern quantum processors---typically used for unitary simulations---as a new experimental platform for dissipative quantum chaos.

[1] Sá, Ribeiro, Prosen, Phys. Rev. X 10, 021019 (2020).

[2] Wold, Zhu, Jin, Zhu, Bao, Zhong, Shen, Zhang, Li, Wang, Song, Guo, Denisov, Sá, Wang, Ribeiro, arXiv:2506.04325 (2025).