Quantum reservoir probing of information propagation and scrambling*

Quantum information scrambling refers to the dynamical phenomenon of initially localized quantum information spreading throughout a system [1]. Recently, scrambling has been quantified using out-of-time-order correlators and tripartite mutual information; however, these measures only indicate the presence or absence of scrambling and provide limited insight into how information is scrambled in the Hilbert space and time. In this study, by extending the idea of quantum reservoir computing, we propose a new framework, quantum reservoir probing (QRP), that allows for direct tracing of the dynamics of information propagation in quantum systems [2]. By scanning the read-out operators employed in the QRP, we can estimate the dynamical distribution of information across multiple degrees of freedom, probing relevant information propagation channels. Indeed, in the quantum Ising chain with transverse and longitudinal magnetic fields, the QRP has deduced two distinct types of information propagation: quasiparticle-mediated propagation in an integrable free fermion system and correlation-mediated scrambling in a quantum chaotic system. Our study provides an efficient approach for further exploration of the dynamics of quantum information in a plethora of exotic quantum many-body systems.

[1] P. Hayden et al., J. High Energy Phys. 09 (2017) 120. [2] K. Kobayashi et al., arXiv:2308.00898.