arXiv subjects

Kazutaka Takahashi

Publications and source records attributed to Kazutaka Takahashi.

At least 19 recordsLinked to original sources

arXiv2026

Krylov Complexity Under Hamiltonian Deformations and Toda Flows

The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of constructing solvable models from known instances. In doing so, we relate the evolution of deformed and undeformed theories and investigate their complexity. For a certain class of deformations, the resulting Krylov subspace is unchanged, and we observe time evolutions with a reorganized basis. The tridiagonal form of the generator in the Krylov space is maintained, and we obtain generalized Toda equations as a function of the deformation parameters. The imaginary-time-like evolutions can be described by real-time unitary ones. As possible applications, we discuss coherent Gibbs states for thermodynamic systems, for which we analyze the survival probability, spread complexity, Krylov entropy, and associated time-averaged quantities. We further discuss the statistical properties of random matrices and supersymmetric systems for quadratic deformations.

quant-ph↗

arXiv2025

Dynamical quantum phase transition, metastable state, and dimensionality reduction: Krylov analysis of fully connected spin models

We study quenched dynamics of fully-connected spin models. The system is prepared in a ground state of the initial Hamiltonian and the Hamiltonian is suddenly changed to a different form. We apply the Krylov subspace method to map the system onto an effective tridiagonal Hamiltonian. The state is confined in a potential well and is time-evolved by nonuniform hoppings. The dynamical singularities for the survival probability can occur when the state is reflected from a potential barrier. Although we do not observe any singularity in the spread complexity, we find that the entropy exhibits small dips at the singular times. We find that the presence of metastable state affects long-time behavior of the spread complexity, and physical observables. We also observe a reduction of the state-space dimension when the Hamiltonian reduces to a classical form.

quant-ph↗

arXiv2025

Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems.

quant-ph↗

arXiv2024

Adiabatic theorem for classical stochastic processes

We apply adiabatic theorems developed for quantum mechanics to stochastic annealing processes described by the classical master equation with a time-dependent generator. When the instantaneous stationary state is unique and the minimum decay rate g is nonzero, the time-evolved state is basically relaxed to the instantaneous stationary state. By formulating an asymptotic expansion rigorously, we derive conditions for the annealing time T that the state is close to the instantaneous stationary state. Depending on the time dependence of the generator, typical conditions are written as T> const/g^a with 1 const|ln g|/g^2.

cond-mat.stat-mech↗

arXiv2024

Shortcuts to Adiabaticity in Krylov Space

Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term, equivalently the adiabatic gauge potential, is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term.

quant-ph↗

arXiv2023

Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth

Quantum speed limits (QSLs) provide lower bounds on the minimum time required for a process to unfold by using a distance between quantum states and identifying the speed of evolution or an upper bound to it. We introduce a generalization of QSL to characterize the evolution of a general operator when conjugated by a unitary. The resulting operator QSL (OQSL) admits a geometric interpretation, is shown to be tight, and holds for operator flows induced by arbitrary unitaries, i.e., with time- or parameter-dependent generators. The derived OQSL is applied to the Wegner flow equations in Hamiltonian renormalization group theory and the operator growth quantified by the Krylov complexity.

quant-ph↗

arXiv2023

Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes

We extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)] to the classical stochastic processes described by the master equation. We demonstrate that the trace distance between arbitrary evolving states is bounded from above by using a geometrical metric. The geometrical bound reduces to the Fisher information metric for the distance between the time-evolved state and the initial state. We compare the bound in relaxation and annealing processes with a different type of bound known for nonequilibrium thermodynamical systems. For dynamical processes such as annealing and pumping processes, the distance between the time-evolved state and the instantaneous stationary state becomes a proper choice and the bound is represented by the Fisher information metric of the stationary state. The metric is related to the counterdiabatic term defined from the time dependence of the stationary state.

cond-mat.stat-mech↗

arXiv2022

Hibikino-Musashi@Home 2022 Team Description Paper

Our team, Hibikino-Musashi@Home (HMA), was founded in 2010. It is based in Japan in the Kitakyushu Science and Research Park. Since 2010, we have annually participated in the RoboCup@Home Japan Open competition in the open platform league (OPL).We participated as an open platform league team in the 2017 Nagoya RoboCup competition and as a domestic standard platform league (DSPL) team in the 2017 Nagoya, 2018 Montreal, 2019 Sydney, and 2021 Worldwide RoboCup competitions.We also participated in theWorld Robot Challenge (WRC) 2018 in the service-robotics category of the partner-robot challenge (real space) and won first place. Currently, we have 27 members from nine different laboratories within the Kyushu Institute of Technology and the university of Kitakyushu. In this paper, we introduce the activities that have been performed by our team and the technologies that we use.

cs.RO↗

arXiv2022

Counterdiabatic driving for periodically driven open quantum systems

We discuss dynamics of periodically-driven open quantum systems. The time evolution of the quantum state is described by the quantum master equation and the form of the dissipator is chosen so that the instantaneous stationary state is given by the Gibbs distribution. We find that the correlation between the population part and the coherence part of the density operator is induced by an adiabatic gauge potential. Although the introduction of the counterdiabatic term eliminates the correlation, additional correlations prevent a convergence to the Gibbs distribution. We study the performance of the control by the counterdiabatic term. The system has three different scales and the performance strongly depends on the relations among their magnitudes.

quant-ph↗

arXiv2022

Dynamical invariant formalism of shortcuts to adiabaticity

We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients. We discuss how the method allows us to realize adiabatic dynamics and describe a relation to the counterdiabatic formalism. The equation for the dynamical invariant takes a familiar form and is often used in various fields of physics. We introduce examples of Lax pair, quantum brachistochrone, and flow equation.

quant-ph↗

arXiv2022

Dynamical Lee-Yang zeros for continuous-time and discrete-time stochastic processes

We describe classical stochastic processes by using dynamical Lee-Yang zeros. The system is in contact with external leads and the time evolution is described by the two-state classical master equation. The cumulant generating function is written in a factorized form and the current distribution of the system is characterized by the dynamical Lee-Yang zeros. We show that a continuous distribution of zeros is obtained by discretizing the time variable. When the transition probability is a periodically-oscillating function of time, the distribution of zeros splits into many parts. We study the geometric property of the current by comparing the result with that of the adiabatic approximation. We also use the Floquet-Magnus expansion in the continuous-time case to study dynamical effects on the current at the fast-driving regime.

cond-mat.stat-mech↗

arXiv2021

Quantum lower and upper speed limits

We derive generalized quantum speed limit inequalities that represent limitations on the time evolution of quantum states. They are extensions of the original inequality and are applied to the overlap between the time-evolved state and an arbitrary state. We can discuss the lower limit of the overlap, in addition to the upper limit as in the original inequality, which allows us to estimate the minimum time for the evolution toward a target state. The inequalities are written by using an arbitrary reference state and are flexibly used to obtain a tight bound. We demonstrate these properties by using the twisted Landau-Zener model, the Grover Hamiltonian, and a periodically-oscillating Hamiltonian.

quant-ph↗

arXiv2021

Thermodynamics of a continuous quantum heat engine: Interplay between population and coherence

We present a detailed thermodynamic analysis of a three-level quantum heat engine coupled continuously to hot and cold reservoirs. The system is driven by an oscillating external field and is described by the Markovian quantum master equation. We use the general form of the dissipator which is consistent with thermodynamics. We calculate the heat, power, and efficiency of the system for the heat-engine operating regime and also examine the thermodynamic uncertainty relation. The efficiency of the system is strongly dependent on the structure of the dissipator, and the correlations between different levels can be an obstacle for ideal operation. In quantum systems, the heat flux is decomposed into the population and coherent parts. The coherent part is specific to quantum systems, and in contrast to the population part, it cannot be expressed by a simple series expansion in the linear-response regime. We discuss how the interplay between the population and coherent parts affects the performance of the heat engine.

quant-ph↗

arXiv2020

Full counting statistics and fluctuation-dissipation relation for periodically driven two-state systems

We derive the fluctuation theorem for a stochastic and periodically driven system coupled to two reservoirs with the aid of a master equation. We write down the cumulant generating functions for both the current and entropy production in closed compact forms so as to treat the adiabatic and nonadiabatic contributions systematically. We derive the fluctuation theorem by taking into account the time reversal symmetry and the property that the instantaneous currents flowing into the left and the right reservoir are not equal. It is found that the fluctuation-dissipation relation derived from the fluctuation theorem involves an expansion with respect to the time derivative of the affinity.

cond-mat.stat-mech↗

arXiv2020

Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential

Adiabatic gauge potential is the origin of nonadiabatic transitions. In counterdiabatic driving, which is a method of shortcuts to adiabaticity, adiabatic gauge potential can be used to realize identical dynamics to adiabatic time evolution without requiring slow change of parameters. We introduce an algebraic expression of adiabatic gauge potential. Then, we find that the explicit form of adiabatic gauge potential can be easily determined by some algebraic calculations. We demonstrate this method by using a single-spin system, a two-spin system, and the transverse Ising chain. Moreover, we derive a lower bound for fidelity to adiabatic time evolution based on the quantum speed limit. This bound enables us to know the worst case performance of approximate adiabatic gauge potential. We can also use this bound to find dominant terms in adiabatic gauge potential to suppress nonadiabatic transitions. We apply this bound to magnetization reversal of the two-spin system and to quantum annealing of the transverse Ising chain. Adiabatic gauge potential reflects structure of energy eigenstates, and thus we also discuss detection of quantum phase transitions by using adiabatic gauge potential. We find a signature of a quantum phase transition in the transverse Ising chain.

quant-ph↗

arXiv2020

Supporting Expert Close Analysis of Historical Scientific Writings: A Case Study for Near-by Reading

Distant reading methodologies make use of computational processes to aid in the analysis of large text corpora which might not be pliable to traditional methods of scholarly analysis due to their volume. While these methods have been applied effectively to a variety of types of texts and contexts, they can leave unaddressed the needs of scholars in the humanities disciplines like history, who often engage in close reading of sources. Complementing the close analysis of texts with some of the tools of distant reading, such as visualization, can resolve some of the issues. We focus on a particular category of this intersection---which we refer to as near-by reading---wherein an expert engages in a computer-mediated analysis of a text with which they are familiar. We provide an example of this approach by developing a visual analysis application for the near-by reading of 19th-century scientific writings by J. W. von Goethe and A. P. de Candolle. We show that even the most formal and public texts, such as scientific treatises, can reveal unexpressed personal biases and philosophies that the authors themselves might not have recognized.

cs.HC↗

arXiv2020

Performance Evaluation of Adiabatic Quantum Computation via Quantum Speed Limits and Possible Applications to Many-Body Systems

The quantum speed limit specifies a universal bound of the fidelity between the initial state and the time-evolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the time-evolved state. The bound is characterized by the counterdiabatic Hamiltonian and can be used to evaluate the worst case performance of the adiabatic quantum computation. The result is improved by imposing additional conditions and we examine several models to find a tight bound. We also derive a different type of quantum speed limits that is meaningful even when we take the thermodynamic limit. By using solvable spin models, we study how the performance and the bound are affected by phase transitions.

quant-ph↗

arXiv2020

Nonadiabatic Control of Geometric Pumping

We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the nontrivial part of the current is possible even in the nonadiabatic regime. The exact result allows us to find a smooth connection between the adiabatic Berry phase theory at low frequencies and the Floquet theory at high frequencies. We also study how to control the geometric current. Using the method of shortcuts to adiabaticity with the aid of an assisting field, we illustrate that it enhances the current.

cond-mat.stat-mech↗