arXiv subjects

Kaito Kobayashi

Publications and source records attributed to Kaito Kobayashi.

10 recordsLinked to original sources

arXiv2026

Irreducible Geometry of Higher-Order Correlator Families

Programmable quantum simulators are beginning to access correlators of increasing complexity, ranging from four-point out-of-time-ordered correlators to even higher-order many-body correlators. The theoretical framework for interpreting such data, however, remains comparatively underdeveloped. Although a variety of higher-order correlators can be constructed straightforwardly, their physical meaning is often difficult to infer. A further complication is that different correlators are generally not independent: some may be mutually redundant, while others may encode genuinely distinct information. These features make it necessary to analyze correlators not as isolated quantities, but as a structured family. In this work, we develop a geometric framework for the collective analysis of higher-order correlator families. By representing correlators as inner products between operator words, we recast each family as a geometry in operator space. The key idea is to introduce conditioning subspaces that separate this geometry into reducible information, already explained by a chosen resolved sector, and irreducible information, encoded in the residual correlator geometry. Focusing on the latter component, we define irreducible volume profiles that quantify how broadly the unexplained part of a correlator family spreads over independent geometric directions. This perspective leads to several complementary forms of conditioning. Canonical conditioning optimally explains a correlator family. Targeted conditioning fixes the resolved sector to isolate a chosen physical feature. Krylov and cross conditioning extend the framework from a single correlator family to comparisons among correlator geometries. Our framework reveals irreducible structures hidden at the level of individual correlator values and establishes correlator geometry as a higher-level description of quantum many-body dynamics.

quant-ph↗

arXiv2026

Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks

Tensor network methods, most prominently matrix product states (MPS), have become fundamental tools in modern quantum many-body physics. While MPS and extensions like the multiscale entanglement renormalization ansatz (MERA) and tree tensor networks (TTN) efficiently capture area-law entanglement and its logarithmic violations, they inherently struggle to represent highly entangled wavefunctions. Specifically, reaching the volume-law regime typically demands exponential resources within these conventional frameworks. Motivated by this challenge, we propose holographic isometric tensor network states (holographic isoTNS) that simulate quantum lattice models in $D$ spatial dimensions via $(D+1)$-dimensional networks of tensors. The additional dimension substantially enlarges the representational manifold, while isometric constraints on each tensor ensure efficient contractibility. Using one-dimensional systems as testbeds, we analyze the properties of holographic isoTNS. First, we show that randomly initialized holographic isoTNS typically display volume-law entanglement at fixed bond dimension. Second, through analytic constructions and variational optimization, we demonstrate that holographic isoTNS can faithfully describe a broad class of highly entangled yet low-complexity states. In particular, the ansatz can represent arbitrary fermionic Gaussian states, Clifford states, extensions of rainbow states, and certain short-time-evolved states under local evolution. Third, to exploit this expressivity in broader contexts, we implement a time-evolving block decimation (TEBD) algorithm on holographic isoTNS. While the method remains efficient and scalable, error accumulation over TEBD sweeps suggests the need for further algorithmic improvement. Overall, holographic isoTNS broaden the scope of tensor-network methods, opening new avenues to study physics in the volume-law regime.

quant-ph↗

arXiv2025

Maximum Cluster Diameter in Non-Critical Bond Percolation

In this paper, we study independent (Bernoulli) bond percolation in dimensions $d \ge 2$, focusing on the maximum diameter of finite clusters in the non-critical regime ($p\neq p_c$). We prove that the maximum diameter $R_n$ satisfies $R_n / \log n \to \varkappa(p)$ almost surely, where $\varkappa(p)$ is determined by the exponential decay rate $ξ(p)$ of $P_p(0 \leftrightarrow \partial B_n, |\mathcal C_0|<\infty)$. Furthermore, we establish a large deviation principle for the event $\{R_n > ρ\log n\}$ for $ρ> \varkappa (p)$. Finally, we consider the asymptotics of the number of vertices in clusters with large diameters.

math.PR↗

arXiv2025

Edge of Many-Body Quantum Chaos in Quantum Reservoir Computing

Reservoir computing (RC) is a machine learning paradigm that harnesses dynamical systems as computational resources. In its quantum extension -- quantum reservoir computing (QRC) -- these principles are applied to quantum systems, whose rich dynamics broadens the landscape of information processing. In classical RC, optimal performance is typically achieved at the ``edge of chaos," the boundary between order and chaos. Here, we identify its quantum many-body counterpart using the QRC implemented on the celebrated Sachdev-Ye-Kitaev model. Our analysis reveals substantial performance enhancements near two distinct characteristic ``edges": a temporal boundary defined by the Thouless time, beyond which system dynamics is described by random matrix theory, and a parametric boundary governing the transition from integrable to chaotic regimes. These findings establish the ``edge of many-body quantum chaos" as a design guideline for QRC.

quant-ph↗

arXiv2025

Quantum reservoir probing of quantum phase transitions

Quantum phase transitions are highly remarkable phenomena manifesting in quantum many-body systems. However, their precise identifications in equilibrium systems pose significant theoretical and experimental challenges. Thus far, dynamical detection protocols employing global quantum quenches have been proposed, wherein transitions are discerned via global nonequilibrium excitations. In this work, we demonstrate that quantum phase transitions can be detected through localized out-of-equilibrium excitations induced by local quantum quenches. While the resulting dynamics after the quench is influenced by both the local quench operation and the intrinsic dynamics of the quantum system, the effects of the former are exclusively extracted using the cutting-edge framework called quantum reservoir probing (QRP). Through the QRP, we find that the impacts of the local quenches vary across different quantum phases and are significantly suppressed by quantum fluctuations amplified near quantum critical points; consequently, phase boundaries are precisely delineated. We demonstrate that the QRP can detect quantum phase transitions in the paradigmatic integrable and nonintegrable quantum spin systems, and even topological quantum phase transitions, all within the identical framework employing local quantum quenches and single-site observables.

quant-ph↗

arXiv2024

Feedback-driven quantum reservoir computing for time-series analysis

Quantum reservoir computing (QRC) is a highly promising computational paradigm that leverages quantum systems as a computational resource for nonlinear information processing. While its application to time-series analysis is eagerly anticipated, prevailing approaches suffer from the collapse of the quantum state upon measurement, resulting in the erasure of temporal input memories. Neither repeated initializations nor weak measurements offer a fundamental solution, as the former escalates the time complexity while the latter restricts the information extraction from the Hilbert space. To address this issue, we propose the feedback-driven QRC framework. This methodology employs projective measurements on all qubits for unrestricted access to the quantum state, with the measurement outcomes subsequently fed back into the reservoir to restore the memory of prior inputs. We demonstrate that our QRC successfully acquires the fading-memory property through the feedback connections, a critical element in time-series processing. Notably, analysis of measurement trajectories reveal three distinct phases depending on the feedback strength, with the memory performance maximized at the edge of chaos. We also evaluate the predictive capabilities of our QRC, demonstrating its suitability for forecasting signals originating from quantum spin systems.

quant-ph↗

arXiv2024

Quantum reservoir probing: an inverse paradigm of quantum reservoir computing for exploring quantum many-body physics

Quantum reservoir computing (QRC) is a brain-inspired computational paradigm, exploiting natural dynamics of a quantum system for information processing. To date, a multitude of quantum systems have been utilized in the QRC, with diverse computational capabilities demonstrated accordingly. This study proposes a reciprocal research direction: probing quantum systems themselves through their information processing performance in the QRC framework. Building upon this concept, here we develop quantum reservoir probing (QRP), an inverse extension of the QRC. The QRP establishes an operator-level linkage between physical properties and performance in computing. A systematic scan of this correspondence reveals intrinsic quantum dynamics of the reservoir system from computational and informational perspectives. Unifying quantum information and quantum matter, the QRP holds great promise as a potent tool for exploring various aspects of quantum many-body physics. In this study, we specifically apply it to analyze information propagation in a one-dimensional quantum Ising chain. We demonstrate that the QRP not only distinguishes between ballistic and diffusive information propagation, reflecting the system's dynamical characteristics, but also identifies system-specific information propagation channels, a distinct advantage over conventional methods.

quant-ph↗

arXiv2023

Video recognition by physical reservoir computing in magnetic materials

Nonlinear spin dynamics in magnetic materials offers a promising avenue for implementing physical reservoir computing, one of the most accomplished brain-inspired frameworks for information processing. In this study, we investigate the practical utility of magnetic physical reservoirs by assessing their performance in a video recognition task. Leveraging a recently developed spatiotemporal parallelization scheme, our reservoir achieves accurate classifications of previously provided images. Our findings pave the way for the development of visual sensors based on the magnetic physical reservoir computing.

cond-mat.mes-hall↗

arXiv2023

Thermally-robust spatiotemporal parallel reservoir computing by frequency filtering in frustrated magnets

Physical reservoir computing is a framework for brain-inspired information processing that utilizes nonlinear and high-dimensional dynamics in non-von-Neumann systems. In recent years, spintronic devices have been proposed for use as physical reservoirs, but their practical application remains a major challenge, mainly because thermal noise prevents them from retaining short-term memory, the essence of neuromorphic computing. Here, we propose a framework for spintronic physical reservoirs that exploits frequency domain dynamics in interacting spins. Through the effective use of frequency filters, we demonstrate, for a model of frustrated magnets, both robustness to thermal fluctuations and feasibility of frequency division multiplexing. This scheme can be coupled with parallelization in spatial domain even down to the level of a single spin, yielding a vast number of spatiotemporal computational units. Furthermore, the nonlinearity via the exchange interaction allows information processing among different frequency threads. Our findings establish a design principle for high-performance spintronic reservoirs with the potential for highly integrated devices.

cond-mat.mes-hall↗

arXiv2022

Skyrmion and vortex crystals in the Hubbard model

A mutual interplay between the charge and spin degrees of freedom in itinerant magnets leads to a plethora of topological spin textures, such as magnetic skyrmion and vortex crystals, in both centrosymmetric and noncentrosymmetric hosts. Meanwhile, their stabilization has been extensively studied in the system including the classical localized spins. We here study a realization of the skyrmion crystal in the centrosymmetric triangular-lattice Hubbard model, where the itinerant nature of electrons plays a more significant role. By performing the self-consistent mean-field calculations, we find that two types of skyrmion crystals with spatially nonuniform charge modulations appear in the ground state at a zero magnetic field. Moreover, we obtain another noncoplanar vortex crystal phase without a net scalar chirality in the vicinity of the skyrmion crystal phase. We show that the latter vortex crystal exhibits the topological phase transition to a different skyrmion phase in an applied magnetic field. Our results provide a possibility of the skyrmion and vortex crystals in itinerant magnets without the localized moments.

cond-mat.str-el↗