Universal anti-Kibble-Zurek scaling in fully-connected systems

Driven-dissipative kerr lattices with two-photon driving are experimentally relevant systems known to exhibit a symmetry-breaking phase transition, which belongs to the universality class of the thermal Ising model for the parameter regime studied here. In this work, we perform finitesize scaling of this system as it is quenched to the transition and the dynamical critical exponent is found to be compatible with z ≈ 2.18 corresponding with metropolis dynamics in classical simulations. Furthermore, we show that the Liouvillian gap scales with the same exponent, similar to scaling of the Hamiltonian gap at quantum phase transitions in closed systems.

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“…trapped ions [64]. Recently, also anti-Kibble Zurek behavior was found under certain circumstances in open quantum systems [65,66].…”

Section: The Liouvillian Gap Scales With the Same Exponentmentioning

confidence: 90%

Classical critical dynamics in quadratically driven Kerr resonators

Verstraelen

Wouters

2020

Phys. Rev. A

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“…In contrast, for long annealing times, the kink density increases as t a increases. This kind of behavior is often referred to as anti-Kibble-Zurek scaling and can result from environmentally-induced heating [48,49]. Weinberg et al also attribute this latter behavior to the effects of noise, including thermal fluctuations.…”

Section: Discussionmentioning

confidence: 99%

“…Tests of the KZM can also be used to quantitatively assess the performance of a quantum device. Indeed, the KZM scaling is sensitive to, e.g., nonlinear driving schemes [38,39], disorder [40,41], inhomogeneities in the system [42][43][44][45] and decoherence [46][47][48][49]. The use of the KZM to assess the performance of a quantum annealer was studied by Gardas et al [50], focusing on the onedimensional case on two previous generation D-Wave 2X devices, and by Weinberg et al [51] on a current generation D-Wave 2000Q (DW2KQ) device, focusing on the Ising Hamiltonian on the two-dimensional square lattice.…”

Section: Introductionmentioning

confidence: 99%

Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond

Bando,

Susa,

Oshiyama

et al. 2020

Preprint

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The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that the quantum simulator results can indeed be explained by the KZM for opensystem quantum dynamics with certain quantitative deviations from the theory likely caused by factors such as random control errors and transient effects. We also probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks, and again find agreement with the quantum simulator results. This implies that the predictions of generalized KZM theory for an isolated system, applies beyond its original scope to an open system. This amounts to the first experimental observation of previously unknown behavior of a quantum system via quantum simulation. To check whether an alternative, classical interpretation of these results is possible, we used the spin-vector Monte Carlo model, a candidate classical description of the D-Wave device. We find that the degree of agreement with the experimental data from the D-Wave devices is better for the KZM, a quantum theory, than for the classical spin-vector Monte Carlo model, thus favoring a quantum description of the device. Our work provides an experimental test of quantum critical dynamics in an open quantum system, and paves the way to new directions in quantum simulation experiments.

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“…Note that H LMG,eff (g), also corresponds to a low-energy effective description of other critical models [79][80][81][82][83]. 3) for the LMG model with counterdiabatic driving, quenched from g(0)=0 towards the QPT, g(τq)=gc=1, for different total times τq (ωτq=10 2 , 10 1 and 10 0 ).…”

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confidence: 93%

Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity

Puebla,

Deffner,

Campbell

2020

Preprint

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Geometric quantum speed limits quantify the trade-off between the rate with which quantum states can change and the resources that are expended during the evolution. Counterdiabatic driving is a unique tool from shortcuts to adiabaticity to speed up quantum dynamics, while preventing nonequilibrium excitations. We show that the quantum speed limit for counterdiabatically driven systems undergoing quantum phase transitions fully encodes the Kibble-Zurek mechanism by correctly predicting the transition from adiabatic to impulse regimes. Our findings are demonstrated for two paradigmatic scenarios, namely the transverse field Ising and the Lipkin-Meshkov-Glick models.

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Universal anti-Kibble-Zurek scaling in fully-connected systems

Cited by 4 publications

References 82 publications

Classical critical dynamics in quadratically driven Kerr resonators

Classical critical dynamics in quadratically driven Kerr resonators

Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond

Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity

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