Transitions in Entanglement Complexity in Random Circuits

True, Sarah; Hamma, Alioscia

doi:10.22331/q-2022-09-22-818

Cited by 18 publications

(14 citation statements)

References 67 publications

(116 reference statements)

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“…• the scaling of entanglement fluctuations corresponding to those of random states in the Hilbert space, as well as of output states of random circuits using universal resources [43,44].…”

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

“…• the failure of a disentangling algorithm based on Metropolis sampling of Clifford random circuits [32,33,44], whereas states with simple patterns of entanglement can be efficiently disentangled by such annealing methods.…”

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

“…Nonetheless, the complexity of entanglement is generally thought of as stemming from the conjunction of a volume-law scaling for entanglement entropies, and a finite magic. Indeed these properties, along with a universal entanglement spectrum statistics, have been shown to be at the root of the onset of quantum chaos [43,[45][46][47]; the hardness of disentangling algorithms [32,33,44]; the universal behavior of out-of-time-order correlation functions (OTOCs); [34,48,49]; and the hardness of simulatability of quantum many-body systems [37,50].…”

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

“…Indeed it has been shown that output states of random Clifford circuits possess volume law for entanglement just like Haar-random states; however, their entanglement spectrum statistics is not Wigner-Dyson distributed, but rather Poissonian. 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%

“…The ground state of the 1d quantum Ising model does not exhibit a complex entanglement pattern, as its entanglement spectrum statistics is far from the Wigner-Dyson distribution. Indeed, it features also other symptoms of simple entanglement pattern: it is efficiently disentangled by entanglement annealing [32,44], lacks a volume-law scaling for entanglement entropy in spite of the volume-law scaling for stabilizer entropy. This is likely going to be the case for the ground states of most local Hamiltonian, given that an area-law scaling of entanglement (up to logarithmic corrections) is their characteristic feature.…”

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

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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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Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

Section: Introduction a Entanglement And Its Complexitymentioning

confidence: 99%

See 3 more Smart Citations

Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions

Piemontese¹,

Roscilde²,

Hamma³

2022

Preprint

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Non-stabilizerness and entanglement from cat-state injection

Peres,

Wagner,

Galvão

2024

New J. Phys.

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Recently, cat states have been used to heuristically improve the runtime of a classical simulator of quantum circuits based on the diagrammatic ZX-calculus. Here we investigate the use of cat-state injection within the quantum circuit model. We explore a family of cat states, $\left| \mathrm{cat}_m^* \right>$, and describe circuit gadgets using them to concurrently inject non-stabilizerness (also known as magic) and entanglement into any quantum circuit. We provide numerical evidence that cat-state injection does not lead to speed-up in classical simulation. On the other hand, we show that our gadgets can be used to widen the scope of compelling applications of cat states. Specifically, we show how to leverage them to achieve savings in the number of injected qubits, and also to induce scrambling dynamics in otherwise non-entangling Clifford circuits in a controlled manner.

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