Growth of genuine multipartite entanglement in random unitary circuits

Bera, Anindita; Roy, Sudipto Singha

doi:10.1103/physreva.102.062431

Cited by 12 publications

(5 citation statements)

References 81 publications

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“…Eq. (17) shows that K Bd G (k) coincides with the Kitaev chain with non Hermitian hopping. Besides charge conjugation symmetry, this model possesses a chiral symmetry which can be made apparent by rotating to the chiral basis by the unitary transformation R = iτ y :…”

Section: Post-selected Dynamicsmentioning

confidence: 89%

Topological transitions in weakly monitored free fermions

2023

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We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases of distinct topological order. We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. In the presence of unitary dynamics, the two topologically distinct phases are separated by a region with sub-volume scaling of the entanglement entropy. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy. We further show that the phase diagram is qualitatively captured by an analytically tractable non-Hermitian model obtained via post-selecting the measurement outcome. Finally we introduce a partial-post-selection continuous mapping, that uniquely associates topological indices of the non-Hermitian Hamiltonian to the distinct phases of the stochastic measurement-induced dynamics.

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Section: Post-selected Dynamicsmentioning

confidence: 89%

Topological transitions in weakly monitored free fermions

2023

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“…This fitting is very good beyond . Beyond this coupling strength, the dynamics are similar to random unitary circuits with conservation laws 3 , 47 . Indeed, setting the external fields in Eq.…”

Section: Open Evolution Of a Rapidly Entangling Systemmentioning

confidence: 99%

Phase transitions in the classical simulability of open quantum systems

Azad

Hallam

Morley

et al. 2023

Sci Rep

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We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian open system counterpart of the saturation in entanglement found in random circuits with projective or weak measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects. Moreover, if a quantum simulator is in this phase, it cannot simulate with quantum advantage.

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“…While a linear fit is enough to describe the early stage growth, other type of functions could be used for describing the whole evolution. Indeed, in [54] the hyperbolic tangent tanh is used, since it enforces the plateau at S n = 1. We also note that another sigmoidal function which empirically fits the model very well in our simulations is the error function.…”

Section: Entanglement Speedmentioning

confidence: 99%

Entanglement entropy production in Quantum Neural Networks

Ballarin¹,

Mangini²,

Montangero³

et al. 2022

Preprint

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Quantum Neural Networks (QNN) are considered a candidate for achieving quantum advantage in the Noisy Intermediate Scale Quantum computer (NISQ) era. Several QNN architectures have been proposed and successfully tested on benchmark datasets for machine learning. However, quantitative studies of the QNNgenerated entanglement have not been investigated in details, and only for up to few qubits. Tensor network methods allow to emulate quantum circuits with a large number of qubits in a wide variety of scenarios. Here, we employ matrix product states to characterize recently studied QNN architectures with up to fifty qubits showing that their entanglement, measured in terms of entanglement entropy between qubits, tends to that of Haar distributed random states as the depth of the QNN is increased. We show a universal behavior for the entanglement entropy production for any given QNN architecture, consequently we introduce a new measure to characterize the entanglement production in QNNs: the entangling speed. Finally, in agreement with known results in the literature, we argue that the most promising regime for quantum advantage with QNNs is defined by a trade-off between high entanglement and expressibility.

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Growth of genuine multipartite entanglement in random unitary circuits

Cited by 12 publications

References 81 publications

Topological transitions in weakly monitored free fermions

Topological transitions in weakly monitored free fermions

Phase transitions in the classical simulability of open quantum systems

Entanglement entropy production in Quantum Neural Networks

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