Information scrambling in quantum circuits

Mi, Xiao; Roushan, P.; Quintana, Chris; Mandrà, Salvatore; Marshall, Jeffrey; Neill, C.; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C.; Barends, R.; Basso, Joao; Bengtsson, Andreas; Boixo, Sergio; Bourassa, Alexandre; Broughton, Michael; Buckley, Bob B.; Buell, David A.; Burkett, Brian; Bushnell, Nicholas; Chen, Zijun; Chiaro, Benjamin; Collins, Roberto; Courtney, William; Demura, Sean; Derk, Alan R.; Dunsworth, A.; Eppens, Daniel; Erickson, Catherine; Farhi, Edward; Fowler, Austin G.; Foxen, Brooks; Gidney, Craig; Giustina, Marissa; Gross, Jonathan A.; Harrigan, Matthew P.; Harrington, Sean D.; Hilton, Jeremy; Ho, Alan; Hong, Sabrina; Huang, Trent; Huggins, William J.; Ioffe, L. B.; Isakov, Sergei V.; Jeffrey, E.; Zhang, Jiang; Jones, Cody; Kafri, Dvir; Kelly, J.; Kim, Seon; Kitaev, Alexei; Klimov, Paul V.; Korotkov, Alexander N.; Kostritsa, Fedor; Landhuis, David; Laptev, Pavel; Lucero, Erik; Martin, Orion; McClean, Jarrod R.; McCourt, Trevor; McEwen, Matt; Megrant, A.; Miao, Kevin C.; Mohseni, Masoud; Montazeri, Shirin; Mruczkiewicz, Wojciech; Mutus, J.; Naaman, Ofer; Neeley, M.; Newman, Michael; Niu, Murphy Yuezhen; O’Brien, Thomas E.; Opremcak, Alex; Ostby, Eric; Pató, Bálint; Petukhov, A.; Redd, Nicholas; Rubin, Nicholas C.; Sank, D.; Satzinger, Kevin J.; Shvarts, Vladimir; Strain, Doug; Szalay, Marco; Trevithick, Matthew D.; Villalonga, Benjamin; White, Theodore C.; Yao, Z. Jamie; Yeh, P.; Zalcman, Adam; Neven, Hartmut; Aleǐner, I. L.; Kechedzhi, Kostyantyn; Smelyanskiy, Vadim; Chen, Yu

doi:10.1126/science.abg5029

Cited by 203 publications

(112 citation statements)

References 73 publications

(167 reference statements)

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“…More generally, the behavior of F depends on the interaction between the different degrees of freedom [32,33]. The OTOC has been experimentally measured in nuclear magnetic resonance quantum simulators [34][35][36][37], trapped ions [38][39][40] and superconducting qubits [41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Emergent symmetry in Brownian SYK models and charge dependent scrambling

Agarwal

2022

J. High Energ. Phys.

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In this work, we introduce a symmetry-based approach to study the scrambling and operator dynamics of Brownian SYK models at large finite N and in the infinite N limit. We compute the out-of-time-ordered correlator (OTOC) in the Majorana model without charge conservation and the complex model with charge conservation, and demonstrate that in both models taking the random average of the couplings gives rise to emergent symmetry structures. The random averaging exactly maps the operator dynamics of the Majorana model and the complex model to the imaginary time dynamics of an SU(2) spin and an SU(4) spin respectively, which become solvable in the large N limit. Furthermore, the symmetry structure drastically reduces the size of the Hilbert space required to calculate the OTOC from exponential to linear in N, providing full access to the operator dynamics at all times for large finite N. In the case of the complex model with charge conservation, using this approach, we obtain the OTOC within each charge sector both numerically at finite N and analytically in the large N limit. We find that the time scale of the scrambling dynamics for all times and in each sector is characterized by the charge density. Furthermore, after proper rescaling, the OTOC corresponding to different finite charge densities collapses into a single curve at large finite N. In the large N limit, the rescaled OTOCs at finite density are described by the same hydrodynamic equation as in the Majorana case.

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Section: Introductionmentioning

confidence: 99%

Emergent symmetry in Brownian SYK models and charge dependent scrambling

Agarwal

2022

J. High Energ. Phys.

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“…The persistent and synchronized oscillations of the OTOC and Holevo information inside the light cone are attributed to the "local" rather than "global" thermalization and robustness of scarred eigenstates against local perturbations, which are argued in [65] and need future in-depth analytical studies. Experiment proposals.-Recent experimental progress has enabled the measurements of information scrambling dynamics in well-controlled synthetic quantum systems, including nuclear magnetic resonance (NMR) systems [72,73], trapped ions [74][75][76][77] and superconducting qubits [78][79][80][81]. The PXP model can be naturally realized with the Rydberg-atom platform [60,82,83], governed by the following Hamiltonian:…”

Section: (B) For a Sketch]mentioning

confidence: 99%

Quantum Information Scrambling in Quantum Many-body Scarred Systems

Yuan,

Zhang,

Wang

et al. 2022

Preprint

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Quantum many-body scarred systems host special non-thermal eigenstates which support periodic revival dynamics and weakly break the ergodicity. In this paper, we study the quantum information scrambling dynamics in quantum many-body scarred systems, with a focus on the "PXP" model. We use the out-of-time-ordered correlator (OTOC) and Holevo information as measures of the information scrambling, and apply an efficient numerical method based on matrix product operators to compute them up to 41 spins. We find that both the OTOC and Holevo information exhibit a linear light cone and periodic oscillations inside the light cone for initial states within the scarred subspace, which is in sharp contrast to thermal or many-body localized systems. To explain the formation of the linear light cone structure, we provide a perturbation-type calculation based on a phenomenological model. In addition, we demonstrate that the OTOC and Holevo information dynamics of the "PXP" model can be measured using the Rydberg-atom quantum simulators with current experimental technologies, and numerically identify the measurable signatures using experimental parameters.

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“…This task lies at the heart of quantum supremacy experiments [5][6][7][8]. While being computationally advantageous for producing samples (just need to send a 'measure' instruction), the considered distributions are not suitable for industrially relevant advantage [9], though may be helpful in studying related concept such as quantum chaos [10]. Finding a subset of problems with distributions which are both classically-intractable and industrially useful is an open challenge.…”

Section: Introductionmentioning

confidence: 99%

Protocols for Trainable and Differentiable Quantum Generative Modelling

Kyriienko¹,

Paine²,

Elfving³

2022

Preprint

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We propose an approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation. Contrary to existing QGM approaches, we perform training of a DQCbased model, where data is encoded in a latent space with a phase feature map, followed by a variational quantum circuit. We then map the trained model to the bit basis using a fixed unitary transformation, coinciding with a quantum Fourier transform circuit in the simplest case. This allows fast sampling from parametrized distributions using a single-shot readout. Importantly, latent space training provides models that are automatically differentiable, and we show how samples from solutions of stochastic differential equations (SDEs) can be accessed by solving stationary and time-dependent Fokker-Planck equations with a quantum protocol. Finally, our approach opens a route to multidimensional generative modelling with qubit registers explicitly correlated via a (fixed) entangling layer. In this case quantum computers can offer advantage as efficient samplers, which perform complex inverse transform sampling enabled by the fundamental laws of quantum mechanics. On a technical side the advances are multiple, as we introduce the phase feature map, analyze its properties, and develop frequency-taming techniques that include qubit-wise training and feature map sparsification.

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Information scrambling in quantum circuits

Cited by 203 publications

References 73 publications

Emergent symmetry in Brownian SYK models and charge dependent scrambling

Emergent symmetry in Brownian SYK models and charge dependent scrambling

Quantum Information Scrambling in Quantum Many-body Scarred Systems

Protocols for Trainable and Differentiable Quantum Generative Modelling

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