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arXiv · 2202.02648

Transitions in Entanglement Complexity in Random Circuits

Sarah True·Alioscia Hamma
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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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Sarah True, Alioscia Hamma. 2022-09-20. Transitions in Entanglement Complexity in Random Circuits. https://doi.org/10.22331/q-2022-09-22-818

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