The idea of studying chaotic quantum dynamics by measuring the spreading of operators under evolution by random quantum circuits, particularly by looking at the evolution of out of time order correlators (OTOCs), has been a topic of recent interest. It turns out that operator spreading under random quantum circuits obeys classical “hydrodynamic” equations, with initially localized operators spreading at a so-called “butterfly velocity” that is less than the light cone velocity of the circuits, and with the front of the operator region broadening diffusively. In this talk, I will go over arguments for these results in one and two dimensional spin systems, and mention the results of an exact calculation for OTOCs in 1D. Next, we will look at how for the calculation of averaged OTOCs, the results from the usual Harr-random circuits agree with the results from Clifford circuits, a simpler kind of quantum circuit that leads to classically simulatable dynamics. I will also talk about the effect of conservation laws on the dynamics of operator spreading.
Note: this event will be hybrid. The live talk occuring in Loomis 276 will be simultaneously broadcast via Zoom. The Zoom link will be sent to the Graduate Student and PDRA mailing lists. If you are not on one of those lists and are interested in attending, please email Cat Kengle at ckengle2@illinois.edu for the link.
