Transitions in Entanglement Complexity in Random Circuits

• URL: http://arxiv.org/abs/2202.02648v4
• Date: Tue, 20 Sep 2022 16:01:24 GMT
• Title: Transitions in Entanglement Complexity in Random Circuits
• Authors: Sarah True, Alioscia Hamma
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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