Verified quantum information scrambling

Quantum information scrambling in two-dimensional Bose-Hubbard lattices

It is a well-understood fact that the transport of excitations throughout a lattice is intimately governed by the underlying structures. Hence, it is only natural to recognize that the dispersion of information also has to depend on the lattice geometry. In the present work, we demonstrate that two-dimensional lattices described by the Bose-Hubbard model exhibit information scrambling for systems as little as two hexagons. However, we also find that the out-of-time-ordered correlator (OTOC) shows the exponential decay characteristic for quantum chaos only for a judicious choice of local observables. More generally, the OTOC is better described by Gaussian-exponential convolutions, which alludes to the close similarity of information scrambling and decoherence theory.

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.

Signature of Scramblon Effective Field Theory in Random Spin Models

Information scrambling refers to the propagation of information throughout a quantum system. Its study not only contributes to our understanding of thermalization but also has wide implications in quantum information and black hole physics. Recent studies suggest that information scrambling in large-N systems with all-to-all interactions is mediated by collective modes called scramblons. However, a criterion for the validity of scramblon theory in a specific model is still missing. In this work, we address this issue by investigating the signature of the scramblon effective theory in random spin models with all-to-all interactions. We demonstrate that, in scenarios where the scramblon description holds, the late-time operator size distribution can be predicted from its early-time value, requiring no free parameters. As an illustration, we examine whether Brownian circuits exhibit a scramblon description and obtain a positive confirmation both analytically and numerically. Our findings provide a concrete experimental framework for unraveling the scramblon field theory in random spin models using quantum simulators.

Classical route to ergodicity and scarring in collective quantum systems

Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.

Finite-Time Teleportation Phase Transition in Random Quantum Circuits

How long does it take to entangle two distant qubits in a quantum circuit evolved by generic unitary dynamics? We show that if the time evolution is followed by measurements of all but two infinitely separated test qubits, then the entanglement between them can undergo a phase transition and become nonzero at a finite critical time t_{c}. The fidelity of teleporting a quantum state from an input qubit to an infinitely distant output qubit shows the same critical onset. Specifically, these finite-time transitions occur in short-range interacting two-dimensional random unitary circuits and in sufficiently long-range interacting one-dimensional circuits. The phase transition is understood by mapping the random continuous-time evolution to a finite-temperature thermal state of an effective spin Hamiltonian, where the inverse temperature equals the evolution time in the circuit. In this framework, the entanglement between two distant qubits at times t>t_{c} corresponds to the emergence of long-range ferromagnetic spin correlations below the critical temperature. We verify these predictions using numerical simulation of Clifford circuits and propose potential realizations in existing platforms for quantum simulation.

Operator Growth in Open Quantum Systems

The spreading of quantum information in closed systems, often termed scrambling, is a hallmark of many-body quantum dynamics. In open systems, scrambling competes with noise, errors, and decoherence. Here, we provide a universal framework that describes the scrambling of quantum information in open systems: we predict that the effect of open-system dynamics is fundamentally controlled by operator size distributions and independent of the microscopic error mechanism. This framework allows us to demonstrate that open quantum systems exhibit universal classes of information dynamics that fundamentally differ from their unitary counterparts. Implications for the Loschmidt echo, nuclear magnetic resonance experiments, and the classical simulability of open quantum dynamics will be discussed.

General Class of Continuous Variable Entanglement Criteria

We present a general class of entanglement criteria for continuous variable systems. Our criteria are based on the Husimi Q distribution and allow for optimization over the set of all concave functions rendering them extremely general and versatile. We show that several entropic criteria and second moment criteria are obtained as special cases. Our criteria reveal entanglement of families of states undetected by any commonly used criteria and provide clear advantages under typical experimental constraints such as finite detector resolution and measurement statistics.

The QBIT theory of consciousness: Entropy and qualia

The QBIT theory is a recently introduced multi-disciplinary approach to the problem of consciousness. One of the main axioms of the theory is that when information-theoretic certainty of an observer about a stimulus goes beyond a certain threshold, the observer becomes conscious of that stimulus. This axiom could provide an explanation for how the brain generates consciousness.In short, the QBIT theory suggests that the brain generates consciousness by reducing the entropy of its internal representations below a critical threshold. This paper explains how the brain gradually minimizes the entropy of its internal representations and consequently generate minimum-entropy representations (also known as conscious representations or qualia). The paper also explores the consequences of this entropy-minimization process in the context of quantum information theory.

Improving metrology with quantum scrambling

Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.

Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment

In closed generic many-body systems, unitary evolution disperses local quantum information into highly nonlocal objects, resulting in thermalization. Such a process is called information scrambling, whose swiftness is quantified by the operator size growth. However, the impact of couplings to the environment on the process of information scrambling remains unexplored for quantum systems embedded within an environment. Here we predict a dynamical transition in quantum systems with all-to-all interactions accompanied by an environment, which separates two phases. In the dissipative phase, information scrambling halts as the operator size decays with time, while in the scrambling phase, dispersion of information persists, and the operator size grows and saturates to an O(N) value in the long-time limit with N the number of degrees of freedom of the systems. The transition is driven by the competition between the system's intrinsic and environment propelled scramblings and the environment-induced dissipation. Our prediction is derived from a general argument based on epidemiological models and demonstrated analytically via solvable Brownian Sachdev-Ye-Kitaev models. We provide further evidence which suggests that the transition is generic to quantum chaotic systems when coupled to an environment. Our study sheds light on the fundamental behavior of quantum systems in the presence of an environment.

Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Dynamical aspects

The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Gamito et al., Phys. Rev. E 106, 044125 (2022)2470-004510.1103/PhysRevE.106.044125]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.

Controlling Local Thermalization Dynamics in a Floquet-Engineered Dipolar Ensemble

Understanding the microscopic mechanisms of thermalization in closed quantum systems is among the key challenges in modern quantum many-body physics. We demonstrate a method to probe local thermalization in a large-scale many-body system by exploiting its inherent disorder and use this to uncover the thermalization mechanisms in a three-dimensional, dipolar-interacting spin system with tunable interactions. Utilizing advanced Hamiltonian engineering techniques to explore a range of spin Hamiltonians, we observe a striking change in the characteristic shape and timescale of local correlation decay as we vary the engineered exchange anisotropy. We show that these observations originate from the system's intrinsic many-body dynamics and reveal the signatures of conservation laws within localized clusters of spins, which do not readily manifest using global probes. Our method provides an exquisite lens into the tunable nature of local thermalization dynamics and enables detailed studies of scrambling, thermalization, and hydrodynamics in strongly interacting quantum systems.

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

A detailed numerical study reveals that the asymptotic values of the standard-deviation-to-mean ratio of the out-of-time-ordered correlator in energy eigenstates can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely, the algebraic u(3) model, and demonstrate a clear correspondence between the energy-smoothed relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a chaos indicator.

Long-Range Bell States from Local Measurements and Many-Body Teleportation without Time Reversal

In this Letter, we study quantum many-body teleportation, where a single qubit is teleported through a strongly interacting quantum system, as a result of a scrambling unitary and local measurements on a few qubits. Usual many-body teleportation protocols require a double copy of the system, and backward time evolution, we demonstrate that teleportation is possible in the 2D spin-1/2 XY model, without these constraints. The necessary long-range entanglement for teleportation is generated from the model hosting special eigenstates known as rainbow scars. We outline a specific protocol for preparing this highly entangled state by evolving a product state and performing iterative measurements on only two qubits with feedback control.

Relaxation Exponents of OTOCs and Overlap with Local Hamiltonians

OTOC has been used to characterize the information scrambling in quantum systems. Recent studies have shown that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In particular, the slow scrambling of OTOC is seen for observables that have an overlap with local conserved quantities. However, an observable may not overlap with the Hamiltonian but instead with the Hamiltonian elevated to an exponent larger than one. Here, we show that higher exponents correspond to faster relaxation, although still algebraic, and such exponents can increase indefinitely. Our analytical results are supported by numerical experiments.

Traversable wormhole dynamics on a quantum processor

The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality¹ is the principal example of holography. The Sachdev-Ye-Kitaev (SYK) model of N ≫ 1 Majorana fermions^2,3 has features suggesting the existence of a gravitational dual in AdS₂, and is a new realization of holography^4-6. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry^7,8 through the traversable wormhole mechanism as implemented in the SYK model^9,10. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol⁹. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits⁹. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding^11-13, coupling on either side of the wormhole that is consistent with a negative energy shockwave¹⁴, a Shapiro time delay¹⁵, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics^16,17. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals¹⁸ and other SYK-like models¹⁹.

Demonstration of Tunable Three-Body Interactions between Superconducting Qubits

Nonpairwise multiqubit interactions present a useful resource for quantum information processors. Their implementation would facilitate more efficient quantum simulations of molecules and combinatorial optimization problems, and they could simplify error suppression and error correction schemes. Here, we present a superconducting circuit architecture in which a coupling module mediates two-local and three-local interactions between three flux qubits by design. The system Hamiltonian is estimated via multiqubit pulse sequences that implement Ramsey-type interferometry between all neighboring excitation manifolds in the system. The three-local interaction is coherently tunable over several MHz via the coupler flux biases and can be turned off, which is important for applications in quantum annealing, analog quantum simulation, and gate-model quantum computation.

Probing Operator Spreading via Floquet Engineering in a Superconducting Circuit

Operator spreading, often characterized by out-of-time-order correlators (OTOCs), is one of the central concepts in quantum many-body physics. However, measuring OTOCs is experimentally challenging due to the requirement of reversing the time evolution of systems. Here we apply Floquet engineering to investigate operator spreading in a superconducting 10-qubit chain. Floquet engineering provides an effective way to tune the coupling strength between nearby qubits, which is used to demonstrate quantum walks with tunable couplings, reversed time evolution, and the measurement of OTOCs. A clear light-cone-like operator propagation is observed in the system with multiple excitations, and has a nearly equal velocity as the single-particle quantum walk. For the butterfly operator that is nonlocal (local) under the Jordan-Wigner transformation, the OTOCs show distinct behaviors with (without) a signature of information scrambling in the near integrable system.

Determination of Multimode Motional Quantum States in a Trapped Ion System

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.

Benchmarking Information Scrambling

Information scrambling refers to the rapid spreading of initially localized information over an entire system, via the generation of global entanglement. This effect is usually detected by measuring a temporal decay of the out-of-time order correlators. However, in experiments, decays of these correlators suffer from fake positive signals from various sources, e.g., decoherence due to inevitable couplings to the environment, or errors that cause mismatches between the purported forward and backward evolutions. In this Letter, we provide a simple and robust approach to single out the effect of genuine scrambling. This allows us to benchmark the scrambling process by quantifying the degree of the scrambling from the noisy backgrounds. We also demonstrate our protocol with simulations on IBM cloud-based quantum computers.

Observation of Thermalization and Information Scrambling in a Superconducting Quantum Processor

Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the XX-ladder model and the one-dimensional XX model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the XX ladder. In contrast, we show that the XX chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.

Signatures of Quantum Chaos in an Out-of-Time-Order Tensor

Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of interest interacts with a small quantum probe whose dynamical properties identify the chaoticity of the system. Specifically, we propose a fully quantum version of the out-of-time-order correlator-which we term the out-of-time-order tensor-whose correlations offer clear information theoretic meanings about the chaoticity of a process. We illustrate the utility of the out-of-time-order tensor as a signature of chaos using random unitary processes as well as in the quantum kicked rotor, where the chaoticity is tunable.

Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature

Out-of-time-ordered correlators (OTOCs) are a key observable in a wide range of interconnected fields including many-body physics, quantum information science, and quantum gravity. Measuring OTOCs using near-term quantum simulators will extend our ability to explore fundamental aspects of these fields and the subtle connections between them. Here, we demonstrate an experimental method to measure OTOCs at finite temperatures and use the method to study their temperature dependence. These measurements are performed on a digital quantum computer running a simulation of the transverse field Ising model. Our flexible method, based on the creation of a thermofield double state, can be extended to other models and enables us to probe the OTOC's temperature-dependent decay rate. Measuring this decay rate opens up the possibility of testing the fundamental temperature-dependent bounds on quantum information scrambling.

Quantum simulation of operator spreading in the chaotic Ising model

There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a four-spin Ising model as a function of space, time, and integrability. Reaching four spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of a ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.

Dissipation-Induced Information Scrambling in a Collision Model

In this paper, we present a collision model to stroboscopically simulate the dynamics of information in dissipative systems. In particular, an all-optical scheme is proposed to investigate the information scrambling of bosonic systems with Gaussian environmental states. Varying the states of environments, in the presence of dissipation, transient tripartite mutual information of system modes may show negative value, signaling the appearance of information scrambling. We also find that dynamical indivisibility based non-Markovianity plays dual roles in affecting the dynamics of information.

Floquet Hamiltonian engineering of an isolated many-body spin system

[Figure: see text].

Information scrambling in quantum circuits

[Figure: see text].

Lieb-Robinson Light Cone for Power-Law Interactions

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/r^{α} at distance r? Here, we present a definitive answer to this question for all exponents α>2d and all spatial dimensions d. Schematically, information takes time at least r^{min{1,α-2d}} to propagate a distance r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

Conditionally Rigorous Mitigation of Multiqubit Measurement Errors

Several techniques have been recently introduced to mitigate errors in near-term quantum computers without the overhead required by quantum error correcting codes. While most of the focus has been on gate errors, measurement errors are significantly larger than gate errors on some platforms. A widely used transition matrix error mitigation (TMEM) technique uses measured transition probabilities between initial and final classical states to correct subsequently measured data. However from a rigorous perspective, the noisy measurement should be calibrated with perfectly prepared initial states, and the presence of any state-preparation error corrupts the resulting mitigation. Here we develop a measurement error mitigation technique, a conditionally rigorous TMEM, that is not sensitive to state-preparation errors and thus avoids this limitation. We demonstrate the importance of the technique for high-precision measurement and for quantum foundations experiments by measuring Mermin polynomials on IBM Q superconducting qubits. An extension of the technique allows one to correct for both state-preparation and measurement (SPAM) errors in expectation values as well; we illustrate this by giving a protocol for fully SPAM-corrected quantum process tomography.

Entanglement entropy and out-of-time-order correlator in the long-range Aubry-André-Harper model

We investigate the nonequilibrium dynamics of entanglement entropy and out-of-time-order correlator (OTOC) of noninteracting fermions at half-filling starting from a product state to distinguish the delocalized, multifractal (in the limit of nearest neighbor hopping), localized and mixed phases hosted by the quasiperiodic Aubry-André-Harper (AAH) model in the presence of long-range hopping. For sufficiently long-range hopping strength a secondary logarithmic behavior in the entanglement entropy is found in the mixed phases whereas the primary behavior is a power-law the exponent of which is different in different phases. The saturation value of entanglement entropy in the delocalized, multifractal and mixed phases depends linearly on system size whereas in the localized phase (in the short-range regime) it is independent of system size. The early-time growth of OTOC shows very different power-law behaviors in the presence of nearest neighbor hopping and long-range hopping. The late time decay of OTOC leads to noticeably different power-law exponents in different phases. The spatial profile of OTOC and its system-size dependence also provide distinct features to distinguish phases. In the mixed phases the spatial profile of OTOC shows two different dependences on space for small and large distances respectively. Interestingly the spatial profile contains large fluctuations at the special locations related to the quasiperiodicity parameter in the presence of multifractal states.

Nonlinear dynamics and quantum chaos of a family of kicked p-spin models

We introduce kicked p-spin models describing a family of transverse Ising-like models for an ensemble of spin-1/2 particles with all-to-all p-body interaction terms occurring periodically in time as delta-kicks. This is the natural generalization of the well-studied quantum kicked top (p=2) [Haake, Kuś, and Scharf, Z. Phys. B 65, 381 (1987)10.1007/BF01303727]. We fully characterize the classical nonlinear dynamics of these models, including the transition to global Hamiltonian chaos. The classical analysis allows us to build a classification for this family of models, distinguishing between p=2 and p>2, and between models with odd and even p's. Quantum chaos in these models is characterized in both kinematic and dynamic signatures. For the latter, we show numerically that the growth rate of the out-of-time-order correlator is dictated by the classical Lyapunov exponent. Finally, we argue that the classification of these models constructed in the classical system applies to the quantum system as well.

Interferometric spectroscopy with quantum light: Revealing out-of-time-ordering correlators

We survey the inclusion of interferometric elements in nonlinear spectroscopy performed with quantum light. Controlled interference of electromagnetic fields coupled to matter can induce constructive or destructive contributions of microscopic coupling sequences (histories) of matter. Since quantum fields do not commute, quantum light signals are sensitive to the order of light-matter coupling sequences. Matter correlation functions are thus imprinted by different field factors, which depend on that order. We identify the associated quantum information obtained by controlling the weights of different contributing pathways and offer several experimental schemes for recovering it. Nonlinear quantum response functions include out-of-time-ordering matter correlators (OTOCs), which reveal how perturbations spread throughout a quantum system (information scrambling). Their effect becomes most notable when using ultrafast pulse sequences with respect to the path difference induced by the interferometer. OTOCs appear in quantum-informatics studies in other fields, including black hole, high energy, and condensed matter physics.

Efficient Stabilized Two-Qubit Gates on a Trapped-Ion Quantum Computer

In order to scale up quantum processors and achieve a quantum advantage, it is crucial to economize on the power requirement of two-qubit gates, make them robust to drift in experimental parameters, and shorten the gate times. Applicable to all quantum computer architectures whose two-qubit gates rely on phase-space closure, we present here a new gate-optimizing principle according to which negligible amounts of gate fidelity are traded for substantial savings in power, which, in turn, can be traded for substantial increases in gate speed and/or qubit connectivity. As a concrete example, we illustrate the method by constructing optimal pulses for entangling gates on a pair of ions within a trapped-ion chain, one of the leading quantum computing architectures. Our method is direct, noniterative, and linear, and, in some parameter regimes, constructs gate-steering pulses requiring up to an order of magnitude less power than the standard method. Additionally, our method provides increased robustness to mode drift. We verify the new trade-off principle experimentally on our trapped-ion quantum computer.

Deterministic Fast Scrambling with Neutral Atom Arrays

Fast scramblers are dynamical quantum systems that produce many-body entanglement on a timescale that grows logarithmically with the system size N. We propose and investigate a family of deterministic, fast scrambling quantum circuits realizable in near-term experiments with arrays of neutral atoms. We show that three experimental tools-nearest-neighbor Rydberg interactions, global single-qubit rotations, and shuffling operations facilitated by an auxiliary tweezer array-are sufficient to generate nonlocal interaction graphs capable of scrambling quantum information using only O(logN) parallel applications of nearest-neighbor gates. These tools enable direct experimental access to fast scrambling dynamics in a highly controlled and programmable way and can be harnessed to produce highly entangled states with varied applications.

Barren Plateaus Preclude Learning Scramblers

Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. We prove a no-go theorem for learning an unknown scrambling process with QML, showing that it is highly probable for any variational Ansatz to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. This implies that the required resources scale exponentially even when strategies to avoid such scaling (e.g., from Ansatz-based barren plateaus or no-free-lunch theorems) are employed. Furthermore, we numerically and analytically extend our results to approximate scramblers. Hence, our work places generic limits on the learnability of unitaries when lacking prior information.

Quantum chaos, equilibration, and control in extremely short spin chains

The environment of an open quantum system is usually modelled as a large many-body quantum system. However, when an isolated quantum system itself is a many-body quantum system, the question of how large and complex it must be to generate internal equilibration is an open key-point in the literature. In this work, by monitoring the degree of equilibration of a single spin through its purity degradation, we are able to sense the chaotic behavior of the generic spin chain to which it is coupled. Quite remarkably, this holds even in the case of extremely short spin chains composed of three spins, where we can also reproduce the whole integrable to chaos transition. Finally, we discuss implications on quantum control experiments and show that quantum chaos reigns over the best degree of control achieved, even in small chains.

Absence of Fast Scrambling in Thermodynamically Stable Long-Range Interacting Systems

In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as R^{-α}, where R is the distance. In such systems, the fast scrambling of quantum information or the exponential growth of information propagation can potentially occur according to the decay rate α. In this regard, a crucial open challenge is to identify the optimal condition for α such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with α>D (D: spatial dimension), where the total energy is extensive in terms of system size and the thermodynamic limit is well defined. We rigorously demonstrate that the OTOC shows a polynomial growth over time as long as α>D and the necessary scrambling time over a distance R is larger than t≳R^{[(2α-2D)/(2α-D+1)]}.

Many-Body Chaos in the Sachdev-Ye-Kitaev Model

Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large N theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev model for up to N=60 Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators. Our procedure accurately determines the Lyapunov exponent, λ, across a wide range in temperatures, including in the regime where λ approaches the universal bound, λ=2π/β.

Detecting Out-of-Time-Order Correlations via Quasiadiabatic Echoes as a Tool to Reveal Quantum Coherence in Equilibrium Quantum Phase Transitions

We propose a new dynamical method to connect equilibrium quantum phase transitions and quantum coherence using out-of-time-order correlations (OTOCs). Adopting the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as illustrative examples, we show that an abrupt change in coherence and entanglement of the ground state across a quantum phase transition is observable in the spectrum of multiple quantum coherence intensities, which are a special type of OTOC. We also develop a robust protocol to obtain the relevant OTOCs using quasi-adiabatic quenches through the ground state phase diagram. Our scheme allows for the detection of OTOCs without time reversal of coherent dynamics, making it applicable and important for a broad range of current experiments where time reversal cannot be achieved by inverting the sign of the underlying Hamiltonian.

An easy to construct sub-micron resolution imaging system

We report an easy to construct imaging system that can resolve particles separated by [Formula: see text] 0.68 [Formula: see text]m with minimum aberrations. Its first photon collecting lens is placed at a distance of 31.6 mm giving wide optical access. The microscope has a Numerical Aperture (NA) of 0.33, which is able to collect signal over 0.36 sr. The diffraction limited objective and magnifier recollects 77% photons into the central disc of the image with a transverse spherical aberration of 0.05 mm and magnification upto 238. The system has a depth of field of 142 [Formula: see text]m and a field of view of 56 [Formula: see text]m which images a large ensemble of atoms. The imaging system gives a diffraction limited performance over visible to near-infrared wavelengths on optimization of the working distance and the distance between the objective and magnifier.

Minimal Model for Fast Scrambling

We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.

Quasi-integrable systems are slow to thermalize but may be good scramblers

Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time-the clearest example being the Solar System-but the situation for their quantum counterparts is less well understood. As a first example, we examine the quantum Lyapunov exponent, defined by the evolution of the four-point out-of-time-order correlator (OTOC), of integrable systems which are weakly perturbed by an external noise, a setting that has proven to be illuminating in the classical case. In analogy to the tangent space in classical systems, we derive a linear superoperator equation which dictates the OTOC dynamics. (1) We find that in the semiclassical limit the quantum Lyapunov exponent is given by the classical one: it scales as ε^{1/3}, with ε being the variance of the random drive, leading to short Lyapunov times compared to the diffusion time (which is ∼ε^{-1}). (2) We also find that in the highly quantal regime the Lyapunov instability is suppressed by quantum fluctuations, and (3) for sufficiently small perturbations the ε^{1/3} dependence is also suppressed-another purely quantum effect which we explain. These essential features of the problem are already present in a rotor that is kicked weakly but randomly. Concerning quantum limits on chaos, we find that quasi-integrable systems are relatively good scramblers in the sense that the ratio between the Lyapunov exponent and kT/ℏ may stay finite at a low temperature T.

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

The evolution with a complex Hamiltonian generally leads to information scrambling. A time-reversed dynamics unwinds this scrambling and thus leads to the original information recovery. We show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.

Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer

The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.

Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions

In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.

Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems

We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension d and the exponent α governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for α≥d+1/2. We also provide a Lévy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1D long-range spin models with 200 sites.

Information Scrambling and Loschmidt Echo

We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator-a recently suggested measure of information scrambling in quantum chaotic systems-and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies.

Does Scrambling Equal Chaos?

Focusing on semiclassical systems, we show that the parametrically long exponential growth of out-of-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model. We derive a lower bound on the OTOC Lyapunov exponent, which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e., for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.

Quantum non-demolition measurement of a many-body Hamiltonian

In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system Hamiltonian, repeated measurements yield the same result and thus minimally disturb the system. Seminal quantum optics experiments have achieved such quantum non-demolition (QND) measurements of systems with few degrees of freedom. In contrast, here we describe how the QND measurement of a complex many-body observable, the Hamiltonian of an interacting many-body system, can be implemented in a trapped-ion analog quantum simulator. Through a single-shot measurement, the many-body system is prepared in a narrow band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis and quantum fluctuation relations.