Onset of scrambling as a dynamical transition in tunable-range quantum circuits

Journal article

In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes. In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior. We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space. This mapping predicts mean-field critical exponents ν=-1/(1+sc), which are consistent with the critical exponents extracted from Clifford-circuit numerics. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.

Authors: Kuriyattil, S; Hashizume, T; Bentsen, G; Daley, AJ

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: PRX Quantum
• Volume: 4
• Issue: 3
• Article number: 030325
• Publication date: 2023-08-23
• Acceptance date: 2023-07-25
• DOI: 10.1103/prxquantum.4.030325
• EISSN: 2691-3399
• Language: English