Quantum Chaos, Non-Stabilizerness, and the Sachdev-Ye-Kitaev Model - Belgrade 06/2025
Abstract
Understanding quantum chaos in many-body systems is crucial to a variety of scientific fields. In statistical physics, the onset of quantum chaos is closely tied to the mechanisms of thermalization. In high-energy physics, chaos and information scrambling play a fundamental role in understanding black hole dynamics. Interestingly, quantum chaos is also relevant to the concept of quantum advantage, i.e. the provable speed-up of algorithms run on quantum hardware. The ability to harness ergodicity and with it, quantum chaos, lies at the core of quantum computing’s transformative potential. In this talk, I will introduce the concept of non-stabilizerness, also known colloquially as „magic“, and discuss its roots in quantum information science. Magic, like entanglement, is a purely quantum resource and plays a crucial role in enabling universal quantum computation. I will also present our recent results (arXiv:2502.03093), where we explored the interplay between entanglement and magic in the Sachdev-Ye-Kitaev (SYK) model – a paradigmatic disordered quantum system with deep connections to the low-dimensional description of black holes. Additionally, I will present new results (arXiv:2505.05199) on the spectral form factor (SFF), a key diagnostic for identifying the onset of quantum chaos in many-body quantum systems. Our analysis exploits a mathematical correspondence between the SFF and random planar walks, offering a novel perspective on its behavior. I will highlight the utility of our recently derived closed-form expression for the plateau (long-time) regime of the SFF in the Sachdev-Ye-Kitaev (SYK) model at various temperatures.
