Transitions in Entanglement Complexity in Random Circuits

TL;DR

This paper investigates how adding T gates to random Clifford circuits induces a transition from simple to complex entanglement patterns, linking entanglement complexity with quantum magic and chaos.

Contribution

It demonstrates numerically that doping Clifford circuits with T gates causes a crossover to complex entanglement, highlighting the role of magic in entanglement complexity.

Findings

Entanglement complexity increases with T gate doping.

Transition from simple to complex entanglement patterns observed.

Complex entanglement linked to quantum magic resources.

Abstract

Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of complexity. The complexity of entanglement is at the root of the onset of quantum chaos, universal distribution of entanglement spectrum statistics, hardness of a disentangling algorithm and of the quantum machine learning of an unknown random circuit, and universal temporal entanglement fluctuations. In this paper, we numerically show how a crossover from a simple pattern of entanglement to a universal, complex pattern can be driven by doping a random Clifford circuit with $T$ gates. This work shows that quantum complexity and complex entanglement stem from the conjunction of entanglement and non-stabilizer resources, also known as magic.