To Learn a Mocking-Black Hole

Leone, Lorenzo; Oliviero, Salvatore F. E.; Piemontese, S.; True, Sarah; Hamma, Alioscia

doi:10.48550/arxiv.2206.06385

Cited by 2 publications

(2 citation statements)

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“…This work shows that entanglement complexity arises from the interplay of magic and entanglement, which has also been shown [37] to be at the root of the onset of complex behavior as revealed by OTOCs [9,66]. We believe that the same mechanism is responsible for a more general transition to complex quantum behavior, for instance in the retrieval of information (or lack thereof) from a black hole [67]. Since the undoing of entanglement is equivalent to the learning of an unknown quantum circuit, the complexity of entanglement also has consequences for the complexity of quantum machine learning algorithms, which is the scope of further investigations.…”

Section: Discussionsupporting

confidence: 63%

Transitions in Entanglement Complexity in Random Circuits

True

Hamma

2022

Quantum

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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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Section: Discussionsupporting

confidence: 63%

Transitions in Entanglement Complexity in Random Circuits

True

Hamma

2022

Quantum

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“…Moreover, the onset of Wigner-Dyson statistics in the output states of random universalcircuits is accompanied by the appearance of universal scaling in the fluctuations of entanglement entropy, while the fluctuations of output states of random Clifford circuits display non-universal scaling [43,44,56] "Simple" entanglement, associated with the absence of magic, has another relevant algorithmic consequence: an entanglement annealing algorithm, which generates a disentangling random Clifford circuit via the Metropolis algorithm, is very efficient in disentangling a state featuring simple entanglement, without any information on the circuit that generated it in the first place. On the other hand, by gradually "doping" random Clifford circuits with universal operations, such as T-gates, one can drive a transition towards a complex pattern of entanglement [43,44,56,57].…”

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions

Piemontese¹,

Roscilde²,

Hamma³

2022

Preprint

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Entanglement comes in different forms, some more complex than others. In this paper we study the transitions of entanglement complexity in an exemplary family of states -the Rokhsar-Kivelson-sign wavefunctions -whose degree of entanglement is controlled by a single parameter. This family of states is known to feature a transition between a phase exhibiting volume-law scaling of entanglement entropy and a phase with sub-extensive scaling of entanglement, reminiscent of the many-bodylocalization transition of disordered quantum Hamiltonians [1]. We study the singularities of the RK-sign wavefunctions and their entanglement complexity across the transition using several tools from quantum information theory: fidelity metric; entanglement spectrum statistics; entanglement entropy fluctuations; stabilizer Rényi Entropy; and the performance of a disentangling algorithm. Across the whole volume-law phase the states feature universal entanglement spectrum statistics. Yet a "super-universal" regime appears for small values of the control parameter in which all metrics become independent of the parameter itself; the entanglement entropy as well as the stabilizer Rényi entropy appear to approach their theoretical maximum; the entanglement fluctuations scale to zero as in output states of random universal circuits, and the disentangling algorithm has essentially null efficiency. All these indicators consistently reveal a complex pattern of entanglement. In the sub-volume-law phase, on the other hand, the entanglement spectrum statistics is no longer universal, entanglement fluctuations are larger and exhibiting a non-universal scaling; and the efficiency of the disentangling algorithm becomes finite. Our results, based on model wavefunctions, suggest that a similar combination of entanglement scaling properties and of entanglement complexity features may be found in high-energy Hamiltonian eigenstates -a very strong candidate being offered by the many-body localization transition of disordered lattice-spin models.

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To Learn a Mocking-Black Hole

Cited by 2 publications

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Transitions in Entanglement Complexity in Random Circuits

Transitions in Entanglement Complexity in Random Circuits

Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions

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