arXiv subjects

Keun-Young Kim

Publications and source records attributed to Keun-Young Kim.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Chaos Diagnostics for non-Hermitian Systems from Bi-Lanczos Krylov Dynamics

In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and out-of-time-order correlators. By contrast, its role in non-Hermitian settings, relevant for modeling open quantum systems, remains less understood due to the challenges posed by complex eigenvalues and the limitations of standard approaches based on orthogonality, such as singular value decomposition. Here we demonstrate that Krylov complexity, computed via the bi-Lanczos algorithm, provides a reliable probe of quantum chaos in non-Hermitian systems, clearly discriminating chaotic and integrable regimes. Our results agree with complex spectral statistics and complex spacing ratios, underscoring the robustness of the method. Universality is supported by extensive tests in the non-Hermitian Sachdev-Ye-Kitaev model and random-matrix ensembles across multiple non-Hermitian symmetry classes, with further validation provided by the non-Hermitian random-field XXZ model as a pseudo-Hermitian system.

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arXiv2026

Deep learning emergent spacetime from fermionic spectral functions in holography

We present a physics-informed machine learning framework based on Neural Ordinary Differential Equations that solves the holographic inverse problem: reconstructing the bulk spacetime and gauge field of a charged AdS black hole directly from boundary fermionic spectral functions. Encoding the UV asymptotics, horizon regularity, and zero temperature extremality as hard constraints in the neural network architecture, our framework reliably reconstructs the extremal Reissner-Nordström AdS geometry across three quantum critical regimes set by the $U(1)$ probe charge---non-Fermi liquid, marginal Fermi liquid (strange metal), and Fermi-liquid-like states---and can jointly infer the probe charge itself to sub-percent accuracy. Relaxing the near-AdS boundary constraint uncovers a geometrical degeneracy: bulk profiles that differ throughout the radial direction but share the same near-horizon $AdS_2 \times \mathbb{R}^2$ data reproduce identical spectral functions near the Fermi surface. This isospectral non-uniqueness is precisely the bulk degeneracy expected on general holographic grounds at zero temperature, and its spontaneous emergence across independent training runs shows that the network isolates the IR CFT universality rather than overfitting a single UV completion.

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arXiv2026

Geometry of quantum states in random matrix ensembles and the chaos-integrability transition

We consider the geometry of quantum states associated with random matrix Hamiltonians belonging to ensembles that exhibit an integrable-to-chaotic transition in terms of the nearest-neighbour energy level spacing distribution, focusing on the $β$-Gaussian ensembles with generic Dyson index. For the tridiagonal Gaussian $β$-ensemble, which shows chaos-to-integrability transition with varying Dyson index, we first calculate an analytical expression for the ensemble-averaged fidelity susceptibility for a two-by-two matrix representation of the Hamiltonian for generic values of the Dyson index, and show that it diverges as the total Hamiltonian, which is the sum of a diagonal matrix with independent elements and a tridiagonal $β$-matrix, goes over to the integrable phase. Next, for large-dimensional matrices, we numerically compute the fidelity susceptibility and the quantum metric tensor, respectively, for a one-parameter and a two-parameter class of Hamiltonians that we construct from the $β$-ensemble, and find scaling relations of these quantities for chaotic and integrable phases. We also consider variations of the $β$-ensemble, such as the one that preserves the rotational invariance of the ensemble, and compute the relevant ensemble-averaged fidelity susceptibility to show that it has similar features as the tridiagonal ensemble in the integrable as well as the chaotic phase, thereby establishing the universality of these properties. Finally, the presence of non-vanishing non-diagonal elements, which arises due to the rotational non-invariance of the $β$-ensembles, is a specific feature of the corresponding metric tensor, and we use this to illuminate the difference between the quantum state space geometry of these ensembles and the rotationally invariant ones, such as the classical Gaussian ensembles.

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arXiv2026

Variational preparation of thermofield double states for SYK models via multi-angle QAOA: sequential angle pruning for circuit reduction

Variational preparation of thermofield double (TFD) states can require deep quantum circuits, particularly for interacting many-body systems. Reducing these circuits while retaining high fidelity is therefore crucial for TFD-state preparation on noisy quantum processors. We study this problem by applying the multi-angle quantum approximate optimization algorithm (ma-QAOA) to TFD-state preparation and introducing two top-down sequential angle-pruning algorithms. Starting from the optimized initial ma-QAOA circuit, both algorithms sequentially remove Pauli-string evolutions with small optimized angles and reoptimize the remaining parameters after each removal. We apply these algorithms to Gaussian and binary Sachdev--Ye--Kitaev (SYK) models in both dense and sparse cases. We find that ma-QAOA prepares the target TFD states with high fidelity and that sequential small-angle pruning retains high fidelity while reducing the circuit depth, particularly at low temperature. Moreover, using the post-reoptimization cost in sequential small-angle pruning further improves the fidelity. For the binary sparse $N=10$ SYK model at $β=10$, $88.8\%$--$92.1\%$ of the nonlocal Pauli-string evolutions are removed while retaining an average fidelity of approximately $95\%$. Finally, we propose extensions of the sequential pruning algorithms toward quantum--classical hybrid implementation.

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arXiv2026

Hayden--Preskill recovery at finite temperature on a quantum processor: dynamics and initial state from the SYK model

In the original Hayden--Preskill recovery, the post-injection scrambler and initial state are {\it not related}. We extend this setup in two ways: by using a SWAP gate so that the scrambler and initial state are {\it related}, and by considering recovery at {\it finite} temperature. For this modified protocol, we show that the information is successfully recovered in the sense that the postselection probability is non-negligible and the conditional fidelity is large. We find that both the postselection probability and the conditional fidelity are proportional to temperature, reflecting the reduced entanglement of the initial state at lower temperatures. We also derive their late-time analytic estimates under the assumption of uniform operator spreading and show that they agree well with the numerical results. This demonstrates that strong scrambling is important for successful information recovery. Implementing the protocol on an IBM superconducting processor using a binary sparse SYK Hamiltonian with $N = 8$ Majoranas, we observe that the data retain the qualitative recovery dynamics and that a SWAP-based error-mitigation scheme improves both the postselection probability and the conditional fidelity.

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arXiv2026

Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy

We introduce generalization of the recently proposed \textit{Latent Entropy} (L-entropy) \cite{Basak:2024uwc} as a refined measure of genuine multipartite entanglement (GME) in pure states of $n$-party quantum systems. Generalized L-entropy provides a natural ordering among $k$-uniform states, maximising for absolutely maximally entangled states (AME), effectively capturing the hierarchical structure of multipartite entanglement. We analyze the behavior of this measure for $n$-party Haar-random states and demonstrate that, in the large local-dimension limit, the maximal L-entropy saturates its upper bound for odd $n$, while for even $n$ it approaches the bound asymptotically. Furthermore, we apply this framework to examine multipartite entanglement properties of quantum states in several variants of the Sachdev-Ye-Kitaev (SYK) model, including SYK$_4$, SYK$_2$, mass-deformed SYK, sparse SYK, and $\mathcal{N}=2$ supersymmetric SYK model. The results demonstrate that the generalized L-entropy serves as a sensitive probe of multipartite entanglement, revealing how deformations influence quantum entanglement structure in such strongly interacting systems.

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arXiv2026

Quantum simulation of traversable-wormhole-inspired quantum teleportation in a chaotic binary sparse SYK model

We report the experimental observation of holographically motivated quantum teleportation on a quantum processor, driven by the highly entangled, chaotic dynamics of a many-body system. Specifically, we implement the traversable-wormhole (TW) protocol utilizing a \textit{chaotic} binary sparse $N = 8$ Sachdev--Ye--Kitaev (SYK) model. This optimized approach dramatically reduces circuit depth for noisy intermediate-scale quantum (NISQ) hardware while rigorously preserving the spectral chaos required for gravitational duality. Diagnosing the teleportation signal via mutual information, we find that while inherent noise in NISQ hardware precludes perfect quantitative agreement with exact numerical simulations, our experimental results clearly demonstrate the essential qualitative signature: a sign-dependent asymmetry. This work establishes a practical, scalable framework for holographic quantum simulations, offering a novel empirical testbed for exploring holographic quantum gravity.

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arXiv2026

Toward Krylov-based holography in double-scaled SYK

Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev model (DSSYK). First, we demonstrate that the growth rate of Krylov state complexity corresponds to the wormhole velocity, and show that its expectation value in coherent states serves as a boundary diagnostic of firewall-like structures via bulk reconstruction. We also delineate an alternative bulk description in terms of the proper momentum of an infalling particle at early times, establishing a threefold duality between the Krylov complexity growth rate, wormhole velocity, and proper momentum, with clear regimes of validity. Beyond the first moments, we argue that higher-order Krylov complexities capture connected bulk contributions encoded by replica wormholes, while the logarithmic variant probes the replica saddle structure. Finally, within a third-quantized setting incorporating baby universes, we show that the Krylov entropy equals the von Neumann entropy of the parent-geometry density matrix obtained after tracing out baby universes, thereby quantifying information flow into the baby universe sector. Together, these results elevate Krylov-space observables to sharp probes of bulk dynamics and topology in ensemble-averaged 2D gravity.

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arXiv2026

Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas

We propose and test logarithmic Krylov (logK) complexity, an operator growth measure akin to Krylov complexity defined through a replica approach, as a viable probe of early-time operator scrambling without false positives. In finite-dimensional quantum systems, such as the Lipkin--Meshkov--Glick (LMG) model and the mixed-field Ising model at the chaotic point, we provide numerical evidence that logK-complexity discriminates between genuine and saddle-dominated scrambling at early times, correctly avoiding the exponential contribution coming from the unstable saddle in the former case, and closely tracking the conventional Krylov complexity in the latter. In integrable quantum systems admitting infinite-dimensional Krylov subspaces, such as the SYK$_{2}$ model and the quantum inverted harmonic oscillator, we show that by modifying the Krylov spreading operator, obtained through generalizing the analytic continuation procedure in the replica trick, the logK complexity can be refined to capture the integrable properties of the theories. We supplement these analyses by extending the Krylov formalism in classical dynamical systems and defining classical versions of these operator growth measures, showing that the false positives arising from unstable saddles in classical phase space are non-existent.

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arXiv2026

A phase space approach to the wavefunction spreading and operator growth in the Krylov basis

In the Wigner-Weyl phase space formulation of quantum mechanics, we analyse the problem of the spreading of an initial state or an initial operator under time evolution when described in terms of the Krylov basis. After constructing the phase space functions corresponding to the Krylov basis states generated by a Hamiltonian from a given initial state by using the Weyl transformation, we subsequently use them to cast the Krylov state complexity as an integral over the phase space in terms of the Wigner function of the time-evolved initial state, so that the contribution of the classical Liouville equation and higher-order quantum corrections to the Wigner function time evolution equation towards the Krylov state complexity can be identified. Next, we construct the double phase space functions associated with the Krylov basis for operators by using a suitable generalisation of the Weyl transformation applicable for superoperators, and use them to rewrite the Krylov operator complexity as an integral over the double phase space in terms of a generalisation of the usual Wigner function. These results, in particular, show that the complexity measures based on the expansion of a time-evolved state (or an operator) in the Krylov basis can be thought to belong to a general class of complexity measures constructed from the expansion coefficients of the time-dependent Wigner function in an orthonormal basis in the phase space, and help us to connect these complexity measures with measures of complexity of time evolved state based on harmonic expansion of the time-dependent Wigner function.

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arXiv2026

Aspects of holographic timelike entanglement entropy in black hole backgrounds

We study the holographic construction of timelike entanglement entropy (tEE) in black hole backgrounds in Lorentzian geometries. The holographic tEE is realized through extremal surfaces consisting of spacelike and timelike branches that encode its real and imaginary components, respectively. In the BTZ black hole, these surfaces extend into the interior of the black hole and reproduce the field-theoretic results. The analysis is further generalized to higher-dimensional AdS-Schwarzschild black holes, where the characteristics of tEE are obtained with increasing size of the boundary subsystem. Besides, we also show that the boundary subsystem length diverges at a dimension-dependent critical turning point. Notably, this critical point moves closer to the black hole horizon as the dimensionality of the bulk increases. For large subsystem lengths, the finite part of the tEE displays a characteristic volume-plus-area structure, with a real volume term and a complex coefficient of the area term approaching constant values at large dimensions. Besides, we also study the monotonicity of a new quantity, timelike entanglement density, which offers insights into a timelike area theorem in specific limits. Subsequently, we investigate the near-horizon dynamics in various black hole backgrounds, where the spacelike and timelike surfaces exhibit exponential growth of the form $e^{\frac{2π}β Δt}$ with inverse black hole temperature $β$.

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arXiv2026

Pole-skipping in the de Sitter horizon structure

We study the pole-skipping structure of incoming waves near the cosmic horizon $r=r_c$ in de Sitter (dS) spacetime. We find that the scalar field with spin-0, the Dirac field with spin-1/2, the Maxwell field with spin-1, the Rarita-Schwinger field with spin-3/2, and the gravitational field with spin-2 exhibit the same frequencies $ω_\star$ of pole-skipping points as their corresponding spin fields satisfying the incoming wave conditions in anti-de Sitter (AdS) spacetime. However, the momenta $k_\star$ undergo a shift in complex space, which originates from the spacetime curvature. The shift in momenta at the pole-skipping points could be measured through the operator dimensions $Δ$ in two curved spacetimes, where momenta are mutually complex conjugate in dS and AdS, two opposite curvature spacetimes.

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arXiv2026

Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum

Motivated by bulk reconstruction of smeared boundary operators, we study the Krylov complexity of local and non-local primary CFT$_d$ operators from the local bulk-to-bulk propagator of a minimally-coupled massive scalar field in Rindler-AdS$_{d+1}$ space. We derive analytic and numerical evidence on how the degree of non-locality in the dual CFT$_d$ observable affects the evolution of Krylov complexity and the Lanczos coefficients. Curiously, the near-horizon limit matches with the same observable for conformally-coupled probe scalar fields inserted at the asymptotic boundary of AdS$_{d+1}$ space. Our results also show that the evolution of the growth rate of Krylov operator complexity in the CFT$_d$ takes the same form as to the proper radial momentum of a probe particle inside the bulk to a good approximation. The exact equality only occurs when the probe particle is inserted in the asymptotic boundary or in the horizon limit. Our results capture a prosperous interplay between Krylov complexity in the CFT, thermal ensembles at finite bulk locations and their role in the holographic dictionary.

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arXiv2025

Quantum Signatures of Chaos from Free Probability

A classical dynamical system can be viewed as a probability space equipped with a measure-preserving time evolution map, admitting a purely algebraic formulation in terms of the algebra of bounded functions on the phase space. Similarly, a quantum dynamical system can be formulated using an algebra of bounded operators in a non-commutative probability space equipped with a time evolution map. Chaos, in either setting, can be characterized by statistical independence between observables at $ t = 0 $ and $ t \to \infty $, leading to the vanishing of cumulants involving these observables. In the quantum case, the notion of independence is replaced by free independence, which only emerges in the thermodynamic limit (asymptotic freeness). In this work, we propose a definition of quantum chaos based on asymptotic freeness and investigate its emergence in quantum many-body systems including the mixed-field Ising model with a random magnetic field, a higher spin version of the same model, and the SYK model. The hallmark of asymptotic freeness is the emergence of the free convolution prediction for the spectrum of operators of the form $ A(0) + B(t) $, implying the vanishing of all free cumulants between $A(0)$ and $B(t)$ in the thermodynamic limit for an infinite-temperature thermal state. We systematically investigate the spectral properties of $ A(0) + B(t) $ in the above-mentioned models, show that fluctuations on top of the free convolution prediction follow universal Wigner-Dyson statistics, and discuss the connection with quantum chaos. Finally, we argue that free probability theory provides a rigorous framework for understanding quantum chaos, offering a unifying perspective that connects many different manifestations of it.

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arXiv2025

Density of states of quantum systems from free probability theory: a brief overview

We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random matrix Hamiltonian, which can be written as a sum of two non-commutating operators, one can obtain an expression for the density of states of the Hamiltonian from the known density of states of the two component operators by assuming that these operators are mutually free and by using the free additive convolution. In many examples of interacting quantum systems and random matrix models, this procedure is known to provide a reasonably accurate approximation to the exact numerical density of states. We review some of the examples that are known in the literature where this procedure works very well, and also discuss some of the limitations of this method in situations where the free probability approximation fails to provide a sufficiently accurate description of the exact density of states. Subsequently, we describe a perturbation scheme that can be developed from the subordination formulas for the Cauchy transform of the density of states and use it to obtain approximate analytical expressions for the density of states in various models, such as the Rosenzweig-Porter random matrix ensemble and the Anderson model with on-site disorder.

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arXiv2025

Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles

Utilizing the framework of free probability, we analyze the spectral and operator statistics of the Rosenzweig-Porter random matrix ensembles, which exhibit a rich phase structure encompassing ergodic, fractal, and localized regimes. Leveraging subordination formulae, we develop a perturbative scheme that yields semi-analytic expressions for the density of states up to second order in system size, in good agreement with numerical results. We compute higher-point correlation functions in the ergodic regime using both numerical and suitable analytic approximations. Our analysis of operator statistics for various spin operators across these regimes reveals close agreement with free probability predictions in the ergodic phase, in contrast to persistent deviations observed in the fractal and localized phases, even at late times. Notably, the fractal phase exhibits partial freeness while retaining memory of the initial spectrum, highlighting the importance of non-localized eigenstates and associated with the late-time dynamics of cumulative out-of-time-ordered-correlators (OTOCs). Employing distance measures and statistical tools such as the $χ^2$ statistic, Kullback-Leibler divergence, and Kolmogorov-Smirnov hypothesis testing, we define a characteristic time scale-the free time-that marks the onset of the validity of free probability predictions for operator spectral statistics in the ergodic phase. Remarkably, our findings demonstrate consistency across these different approaches.

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arXiv2025

AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problems

We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving non-linear differential equations of motion. First, we introduce holographic inverse problems and demonstrate how PIML can reconstruct bulk spacetime and effective potentials from boundary quantum data. To illustrate this, two case studies are explored: the QCD equation of state in holographic QCD and $T$-linear resistivity in holographic strange metals. Additionally, we explicitly show how such holographic problems can be analogized to inverse problems in classical mechanics, modeling frictional forces with neural networks. We also explore Kolmogorov-Arnold Networks (KANs) as an alternative to traditional neural networks, offering more efficient solutions in certain cases. This manuscript aim to provide a systematic framework for using neural networks in inverse problems, serving as a comprehensive reference for researchers in machine learning for high-energy physics, with methodologies that also have broader applications in mathematics, engineering, and the natural sciences.

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arXiv2025

Brickwall model for hyperbolic black holes and chaos

We study the quantum chaotic behavior of black holes within the brickwall model, focusing on probe scalar fields in ($d+1$)-dimensional hyperbolic AdS black holes. The brickwall model has captured the normal modes of BTZ black holes ($d=2$) with Gaussian-distributed boundary conditions on the stretched horizon and their connection to quantum chaos signatures of random matrix theory. Here, we extend this framework to higher-dimensional AdS black holes ($d>2$), exploring how black hole normal modes encode chaotic dynamics across dimensions and examining the universality of this approach. We show that quantum chaos is prominent in lower dimensions and persists in higher dimensions. Specifically, deviations from the logarithmic spectrum in $d=2$ evolves into a power-law spectrum at higher $d$, highlighting the sensitivity of black hole normal modes to dimensionality, while retaining signatures of quantum chaos despite the spectral deformation. Our results are supported by conventional diagnostics, including level spacing distributions and spectral form factors, as well as modern tools like Krylov complexity. Finally, we discuss the limitations of the brickwall model in capturing chaotic behavior in the parametrically large dimension limit, where the spectrum becomes constant leading to degeneracy and a non-chaotic regime, while emphasizing its effectiveness as a tool for studying quantum aspects of black holes in moderate higher dimensions.

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