Probing quantum information propagation with out-of-time-ordered correlators

Braumüller, Jochen; Karamlou, Amir H.; Yanay, Yariv; Kannan, Bharath; Kim, David; Kjærgaard, Morten; Melville, Alexander; Niedzielski, Bethany; Sung, Youngkyu; Vepsäläinen, Antti; Winik, Roni; Yoder, Jonilyn; Orlando, Terry P.; Gustavsson, Simon; Tahan, Charles; Oliver, William

doi:10.1038/s41567-021-01430-w

Cited by 86 publications

(66 citation statements)

References 41 publications

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“…Formally, one can write the above equation in the form OTOC ψ| W † (t)σ x r W (t)σ x r |ψ , using the fact that the state |ψ is an eigenstate of σ x r . This scheme is carried out in [94][95][96] In the previous example, the OTOC is measured with respect to a pure state. To direct measure OTOC for the infinite temperature ensemble, the most straightforward setup is to prepare double copies of the system, such as a ladder.…”

Section: A Rewinding Timementioning

confidence: 99%

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Xu¹,

Swingle²

2022

Preprint

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This tutorial article introduces the physics of quantum information scrambling in quantum manybody systems. The goals are to understand how to quantify the spreading of quantum information precisely and how causality emerges in complex quantum systems. We introduce the general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, in certain circumstances, can be precisely quantified by the so-called out-the-time ordered correlator (OTOC). The general behavior of OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which OTOC is analytically tractable. We introduce numerical methods, both exact diagonalization and tensor network methods, to calculate OTOC for generic quantum many-body systems. We also survey current experiment schemes to measure OTOC in various quantum simulators.

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Section: A Rewinding Timementioning

confidence: 99%

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Xu¹,

Swingle²

2022

Preprint

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“…A lot of attention has been paid to the highest manifold with no multi-boson occupancies at any site. This situation can be effectively described with the so-called hard-core boson model [10,22]. But by choosing the initial state appropriately, one can equally well study any of the other manifolds, each with a different effective model.…”

Section: Transmon Arrays and The Attractive Bose-hubbard Modelmentioning

confidence: 99%

“…Superconducting quantum devices have arisen as a practical platform for creating and studying synthetic quantum matter [1] through, for example, the realizations of a Mott insulator [2] and many-body localization [3][4][5][6][7], as well as for probing the propagation of singleand many-body quantum information [8][9][10][11]. Their remarkable progress has been made possible by universal single-site control, high-accuracy measurements, scalability, and connectivity, all combined with low dissipation and decoherence rates [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…In an array, the hopping rate J between the transmons is weak compared to the anharmonicity U of an individual transmon. As a consequence, the quantum dynamics of the system can be predicted with relatively good accuracy using the hard-core boson model [10,22], provided the initial state has no higher-level occupancies. In other words, the hard-core boson model is the many-body version of the two-level truncation.…”

Section: Introductionmentioning

confidence: 99%

“…In other words, the hard-core boson model is the many-body version of the two-level truncation. Notably, most of the experimental quantum dynamics studies have limited themselves to this case where no transmon is initially excited above the qubit subspace [3,6,8,10,11,16].…”

Section: Introductionmentioning

confidence: 99%

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Beyond hard-core bosons in transmon arrays

Mansikkamäki¹,

Laine²,

Atte³

et al. 2022

Preprint

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Arrays of transmons have proven to be a viable medium for quantum information science and quantum simulations. Despite their widespread popularity as qubit arrays, there remains yet untapped potential beyond the two-level approximation or, equivalently, the hard-core boson model. With the higher excited levels included, coupled transmons naturally realize the attractive Bose-Hubbard model. The dynamics of the model has been difficult to study due to unfavorable scaling of the dimensionality of the Hilbert space with the system size. In this work, we present a framework for describing the effective unitary dynamics of highly-excited states of coupled transmons based on high-order degenerate perturbation theory. This allows us to describe various collective phenomenasuch as bosons stacked onto a single site behaving as a single particle, edge-localization, and effective longer-range interactions -in a unified, compact and accurate manner. While our examples deal with one-dimensional chains of transmons for the sake of clarity, the theory can be readily applied to more general geometries.

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Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry

Agarwal

Sahu

2023

J. High Energ. Phys.

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In this work, we derive an exact hydrodynamical description for the coupled, charge and operator dynamics, in a quantum many-body system with U(1) symmetry. Using an emergent symmetry in the complex Brownian SYK model with charge conservation, we map the operator dynamics in the model to the imaginary-time dynamics of an SU(4) spin-chain. We utilize the emergent SU(4) description to demonstrate that the U(1) symmetry causes quantum-coherence to persist even after disorder-averaging, in sharp contrast to models without symmetries. In line with this property, we write down a ‘restricted’ Fokker-Planck equation for the out-of-time ordered correlator (OTOC) in the large-N limit, which permits a classical probability description strictly in the incoherent sector of the global operator-space. We then exploit this feature to describe the OTOC in terms of a Fisher-Kolmogorov-Petrovsky-Piskun (FKPP)-equation which couples the operator with the charge and is valid at all time-scales and for arbitrary charge-density profiles. The coupled equations obtained belong to a class of models also used to describe the population dynamics of bacteria embedded in a diffusive media. We simulate them to explore operator-dynamics in a background of non-uniform charge configuration, which reveals that the charge transport can strongly affect dynamics of operators, including those that have no overlap with the charge.

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Probing quantum information propagation with out-of-time-ordered correlators

Cited by 86 publications

References 41 publications

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Beyond hard-core bosons in transmon arrays

Charge transport, information scrambling and quantum operator-coherence in a many-body system with U(1) symmetry

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