Transitions in Entanglement Complexity in Random Circuits

Sarah True1 and Alioscia Hamma1,2,3

1Physics Department, University of Massachusetts Boston, 02125, USA
2Dipartimento di Fisica `Ettore Pancini', Università degli Studi di Napoli Federico II, Via Cintia 80126, Napoli, Italy
3INFN, Sezione di Napoli, Italy

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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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Cited by

[1] Tobias Haug and M. S. Kim, "Scalable measures of magic for quantum computers", arXiv:2204.10061.

[2] Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, "Magic hinders quantum certification", arXiv:2204.02995.

[3] Lorenzo Leone, Salvatore F. E. Oliviero, Stefano Piemontese, Sarah True, and Alioscia Hamma, "To Learn a Mocking-Black Hole", arXiv:2206.06385.

[4] J. Odavić, T. Haug, G. Torre, A. Hamma, F. Franchini, and S. M. Giampaolo, "Complexity of frustration: a new source of non-local non-stabilizerness", arXiv:2209.10541.

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