Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalization irreversibility in many-body systems. Here we propose an unconventional mechanism to generate quantum information scrambling through a high-complexity mapping from logical to physical degrees-of-freedom that hides the logical information into nonseparable many-body correlations. Corresponding to this mapping, we develop an algorithm to efficiently sample a Slater-determinant wave function and compute all physical observables in dynamics with a polynomial cost in system size. The system shows information scrambling in the quantum many-body Hilbert space characterized by the spreading of Hamming distance. At late time we find emergence of classical diffusion dynamics in this quantum many-body system. We establish that the operator mapping enabled growth in an out-of-time-order correlator exhibits exponential-scrambling behavior. The quantum information-hiding mapping approach may shed light on the understanding of fundamental connections among computational complexity, information scrambling, and quantum thermalization.
Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalization irreversibility in many-body systems. Here we propose an unconventional mechanism to generate quantum information scrambling through a high-complexity mapping from logical to physical degrees-of-freedom that hides the logical information into nonseparable many-body correlations. Corresponding to this mapping, we develop an algorithm to efficiently sample a Slater-determinant wave function and compute all physical observables in dynamics with a polynomial cost in system size. The system shows information scrambling in the quantum many-body Hilbert space characterized by the spreading of Hamming distance. At late time we find emergence of classical diffusion dynamics in this quantum many-body system. We establish that the operator mapping enabled growth in an out-of-time-order correlator exhibits exponential-scrambling behavior. The quantum information-hiding mapping approach may shed light on the understanding of fundamental connections among computational complexity, information scrambling, and quantum thermalization.
A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.
Abstract The shift from reversible quantum dynamics to irreversible thermodynamics is one of the most complex and at the same time the most important issue in modern physics. A new and efficient method developed by studying black holes and quantum chaos gives the problem stance as one of information dynamics. In this paper, the authors explore the scenario whereby information scrambling is viewed as the micro-level power of quantum thermalization. They start by explaining the most basic paradigms of thermalizing systems that are typified by the eigenstate thermalization hypothesis (ETH) and their non-thermalizing opposites which are characterized by many-body localization. Following that, the authors engage in a comprehensive discussion of the out-of-time-order correlator as the primary tool for diagnosing scrambling, giving a detailed account of its connection with operator spreading, quantum chaos, and the butterfly effect. The central idea that unites this review is that fast, exponential scrambling dynamics bring about ETH and thermalization while a slowdown in scrambling results in localization. An extensive review of the pioneering experiments on trapped-ion, superconducting-qubit, and other quantum-simulation platforms that have clearly witnessed these phenomena is conducted. Ultimately, physicists point out the main unresolved questions and future research paths at the meeting point of quantum gravity, condensed matter, and quantum information science, positioning scrambling as a critical concept for the next few years in many-body physics.
For the characterization of the dynamics in quantum many-body systems the question of how information spreads and becomes distributed over the constituent degrees of freedom is of fundamental interest. The delocalization of information under many-body dynamics has been dubbed scrambling, and out-of-time-order correlators were proposed to probe this behavior. In this work we investigate the time evolution of tripartite information as a natural operator-independent measure of scrambling, which quantifies to what extent the initially localized information can be recovered only by global measurements. Studying the dynamics of quantum lattice models with tunable integrability breaking, we demonstrate that in contrast to quadratic models generic interacting systems scramble information irrespective of the chosen partitioning of the Hilbert space, which justifies the characterization as a scrambler. Without interactions the dynamics of tripartite information in momentum space reveals unambiguously the absence of scrambling.
The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity, and gravity. Here, we extend the framework for exploring information scrambling to infinite-dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: (i) scrambling in the phase space of a single mode and (ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct types of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out, and quasiscrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent, and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed.
This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex quantum systems. We introduce a 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, under certain circumstances, can be precisely quantified by the so-called out-of-time-ordered correlator (OTOC). The general behavior of the OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which the OTOC is analytically tractable. We introduce numerical methods, including exact diagonalization and tensor network methods, to calculate the OTOC for generic quantum many-body systems. We also survey current experimental schemes for measuring the OTOC in various quantum simulators. Published by the American Physical Society 2024