Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator

Li, Jun; Fan, Ruihua; Wang, Hengyan; Ye, Bingtian; Zeng, Bei; Zhai, Hui; Peng, Xinhua; Du, Jiangfeng

doi:10.1103/physrevx.7.031011

Cited by 439 publications

(387 citation statements)

References 46 publications

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“…Recently, new protocols and methods, that are versatile to simulate diverse many-body systems and achievable with state-of-the-art technology, have been proposed to measure the OTOC [14,32]. Furthermore, experimental measurements of the OTOC have also been implemented [33,34]. All these progresses provide test beds for our proposal.…”

Section: Discussionmentioning

confidence: 99%

Holographic butterfly effect at quantum critical points

Ling¹,

Liu²,

Wu³

2017

J. High Energ. Phys.

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When the Lyapunov exponent λ L in a quantum chaotic system saturates the bound λ L 2πk B T , it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).

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Section: Discussionmentioning

confidence: 99%

Holographic butterfly effect at quantum critical points

Ling¹,

Liu²,

Wu³

2017

J. High Energ. Phys.

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“…After the completion of this work, we became aware of measurements of OTOCs using 4 spins in an NMR system [43].…”

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confidence: 99%

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

et al. 2017

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Controllable arrays of ions and ultra-cold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favorably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the manybody dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems.Time-reversal has fascinated and puzzled physicists for centuries. In an iconic example, Josef Loschmidt argued that the second law of thermodynamics would be violated by time-reversing an entropy-increasing collision [1]. Ludwig Boltzmann responded by formulating the probabilistic definition of entropy, one of the cornerstones of statistical mechanics, and, now a fundamental concept in quantum information. Since the days of Boltzmann and Loschmidt, the notion of time-reversal has moved from the arena of thought experiments into the laboratory, with time-reversal of non-interacting quantum systems in the form of Hahn spin echoes [2] forming an essential part of nuclear magnetic resonance (NMR) [3] and magnetic resonance imaging.Recently, the experimental implementation of manybody time-reversal protocols [4,5] in atomic quantum systems have attracted attention [6][7][8][9] for their potential to quantify the flow of quantum information in time and set bounds on thermalization times [10][11][12][13], which might also enable experimental tests of the holographic duality between quantum and gravitational systems [6,[14][15][16][17]. The key quantities sought after are special types of outof-time-order correlation (OTOC) functions,whereŴ (τ ) = e iĤτŴ e −iĤτ , withĤ an interacting many-body Hamiltonian andŴ andV two commuting unitary operators. Physically, F (τ ) measures the "scrambling" of quantum information across the system's manybody degrees of freedom, for example, how fast an initial * These authors contributed equally.† john.bollinger@nist.gov ‡ arey@jila.colorado.edu local perturbation becomes inaccessible to local probesencapsulates the degree by which the initially commuting operatorsŴ andV fail to commute at later times due to the interactions generated byĤ, which we adopt as an operational definition of scrambling.Most theoretical studies of scrambling have focused on so-called fast scramblers in thermal states [10,11,16]...

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“…However, let us assume that these data can be in principle collected, for example by experimental measurements [69][70][71][72] . Then they can be used to construct the training set:…”

Section: Entanglement Feature Learning a General Algorithmmentioning

confidence: 99%

Machine learning spatial geometry from entanglement features

You

Zhao

2018

Phys. Rev. B

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Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).

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Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator

Cited by 439 publications

References 46 publications

Holographic butterfly effect at quantum critical points

Holographic butterfly effect at quantum critical points

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

Machine learning spatial geometry from entanglement features

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