Entanglement Annealing and Fluctuations

As quantum computing has entered the era of NISQ computers, numerical simulations of quantum computational models have grown in popularity as a tool for analyzing and characterizing properties of quantum systems. Among these properties is the transition to quantum chaos observed in random quantum circuits, which can be studied by complexity in the entanglement pattern of quantum states. Understanding the onset of irreversibility and chaotic behavior in quantum evolutions is important both in fundamental theory and in the optimization of the resources needed to develop quantum technology. Entanglement complexity is revealed by the degree of success of an entanglement cooling algorithm, the universality of its fluctuations, and the entanglement spectrum statistics. Previously, it has been shown that random circuits entangle a system to such a level of complexity that it entirely hinders our ability to disentangle it. On the other hand, random Clifford circuits feature non-complex entanglement that can be efficiently undone. In this work, we study the entanglement complexity generated by doping Clifford circuits with non-Clifford resources and show how this drives the transition to universal fluctuations of entanglement and higher entanglement complexity.