arXiv subjects

Yoshihiko Hasegawa

Publications and source records attributed to Yoshihiko Hasegawa.

At least 55 records · Page 3Linked to original sources

arXiv2024

Lie Algebraic Quantum Phase Reduction

We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schrödinger equation. Because a perturbation is represented by unitary transformation in quantum dynamics, we calculate phase response curves with respect to generators of a Lie algebra. Our method shows that the continuous measurement yields phase clusters and alters the phase response curves. The observable clusters capture the phase dynamics of individual quantum oscillators, unlike indirect indicators obtained from density operators. Furthermore, our method can be applied to finite-level systems that lack classical counterparts.

quant-ph↗

arXiv2024

Thermodynamic correlation inequality

Trade-off relations place fundamental limits on the operations that physical systems can perform. This Letter presents a trade-off relation that bounds the correlation function, which measures the relationship between a system's current and future states, in Markov processes. The obtained bound, referred to as the thermodynamic correlation inequality, states that the change in the correlation function has an upper bound comprising the dynamical activity, a thermodynamic measure of the activity of a Markov process. Moreover, by applying the obtained relation to the linear response function, it is demonstrated that the effect of perturbation can be bounded from above by the dynamical activity.

quant-ph↗

arXiv2023

Monomial-agnostic computation of vanishing ideals

In the last decade, the approximate basis computation of vanishing ideals has been studied extensively in computational algebra and data-driven applications such as machine learning. However, symbolic computation and the dependency on term order remain essential gaps between the two fields. In this study, we present the first $\textit{monomial-agnostic}$ basis computation, which works fully numerically with proper normalization and without term order. This is realized by gradient normalization, a newly proposed data-dependent normalization that normalizes a polynomial with the magnitude of gradients at given points. The data-dependent nature of gradient normalization brings various significant advantages: i) efficient resolution of the spurious vanishing problem, the scale-variance issue of approximately vanishing polynomials, without accessing coefficients of terms, ii) scaling-consistent basis computation, ensuring that input scaling does not lead to an essential change in the output, and iii) robustness against input perturbations, where the upper bound of error is determined only by the magnitude of the perturbations. Existing studies did not achieve any of these. As further applications of gradient information, we propose a monomial-agnostic basis reduction method and a regularization method to manage positive-dimensional ideals.

cs.SC↗

arXiv2023

Quantum thermodynamic uncertainty relation under feedback control

The thermodynamic uncertainty relation posits that higher thermodynamic costs are essential for a system to function with greater precision. Recent discussions have expanded thermodynamic uncertainty relations beyond classical non-equilibrium systems, investigating how quantum characteristics can be utilized to improve precision. In this Letter, we explore how quantum feedback, a control technique used to manipulate quantum systems, can enhance the precision. Specifically, we derive a quantum thermodynamic uncertainty relation for feedback control under jump measurement, which provides the lower bound to the scaled variance of the number of jumps. We find that the presence of feedback control can increase the accuracy of continuous measured systems, which is verified with numerical simulations. Moreover, we derive a quantum thermodynamic uncertainty relation for feedback control under homodyne detection.

quant-ph↗

arXiv2023

Upper bound for entropy production in Markov processes

The second law of thermodynamics states that entropy production cannot be negative. Recent developments concerning uncertainty relations in stochastic thermodynamics, such as thermodynamic uncertainty relations and speed limits, have yielded refined second laws that provide lower bounds of entropy production by incorporating information from current statistics or distributions. In contrast, in this study, we bound the entropy production from above by terms comprising the dynamical activity and maximum transition-rate ratio. We derive two upper bounds: one applies to steady-state conditions, whereas the other applies to arbitrary time-dependent conditions. We verify these bounds through numerical simulation and identify several potential applications.

cond-mat.stat-mech↗

arXiv2023

Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence

The bulk-boundary correspondence provides a guiding principle for tackling strongly correlated and coupled systems. In the present work, we apply the concept of the bulk-boundary correspondence to thermodynamic bounds described by classical and quantum Markov processes. Using the continuous matrix product state, we convert a Markov process to a quantum field, such that jump events in the Markov process are represented by the creation of particles in the quantum field. Introducing the time evolution of the continuous matrix product state, we apply the geometric bound to its time evolution. We find that the geometric bound reduces to the speed limit relation when we represent the bound in terms of the system quantity, whereas the same bound reduces to the thermodynamic uncertainty relation when expressed based on quantities of the quantum field. Our results show that the speed limit and thermodynamic uncertainty relations are two aspects of the same geometric bound.

cond-mat.stat-mech↗

arXiv2023

Quantum Otto cycle under strong coupling

Quantum heat engines are often discussed under the weak coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak coupling assumption is proposed. We replace the thermalization process in the weak coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and it indicates that when the contribution of the interaction terms is neglected in the weak interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak coupling counterpart.

quant-ph↗

arXiv2023

ISAAQ: Ising Machine Assisted Quantum Compiler

It is imperative to compile quantum circuits for Noisy Intermediate-Scale Quantum (NISQ) devices because of the limited connectivity of physical qubits and the high error rates of gate operations. One of the most critical steps in quantum circuit compilation is qubit routing, an NP-Hard problem that involves placing and moving logical qubits to minimize compilation overhead. In this study, we propose ISing mAchine Assisted Quantum compiler (ISAAQ) to perform qubit routing with Ising machines, which can efficiently solve Quadratic Unconstrained Binary Optimization (QUBO) problems. ISAAQ accurately estimates the compilation costs by updating itself using previous compilation results, and accelerates qubit routing by solving QUBO problems in parallel with multiple Ising machines. In addition, ISAAQ exploits a cost-reduction method that implements commutative logical Controlled-NOT (CNOT) gates with fewer physical CNOT gates, which is particularly effective for planar devices when implementing original gates. Experimental results on both IBM QX5 and IBM QX20 show that ISAAQ outperforms the heuristic methods available in Qiskit and tket, as well as an existing QUBO method, requiring fewer physical CNOT gates for most benchmark circuits. ISAAQ performs particularly well on large circuits, demonstrating its strong scalability with respect to the number of logical CNOT gates.

quant-ph↗

arXiv2023

Relativistic entropy production for quantum field in cavity

A nonuniformly accelerated quantum field in a cavity undergoes the coordinate transformation of annihilation and creation operators, known as the Bogoliubov transformation. This study considers the entropy production of a quantum field in a cavity induced by the Bogoliubov transformation. By classifying the modes in the cavity into the system and environment, we obtain the lower bound of the entropy production, defined as the sum of the von Neumann entropy in the system and the heat dissipated to the environment. This lower bound represents the refined second law of thermodynamics for a quantum field in a cavity and can be interpreted as the Landauer principle, which yields the thermodynamic cost of changing information contained within the system. Moreover, it provides an upper bound for the quantum mutual information to quantify the extent of the information scrambling in the cavity due to acceleration.

cond-mat.stat-mech↗

arXiv2022

Uncertainty relation for indirect measurement

Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate observables. While measurement uncertainty has been established for the accuracy of quantum measurement, thermodynamic uncertainty is being researched as a new perspective on the accuracy of fluctuating observables that trades off a physical cost in the classical or quantum regime. Following these ideas, we derive a new measurement uncertainty with respect to indirect measurement in the light of quantum thermodynamics. The obtained result shows a reciprocal relation between a survival activity, which is a frenetic contribution to the thermodynamic system, and noise due to the measurement approach. Moreover, this uncertainty can also affect the disturbance of an incompatible counterpart through the universal noise-disturbance relation.

quant-ph↗

arXiv2022

Unified thermodynamic-kinetic uncertainty relation

Understanding current fluctuations is of fundamental importance and paves the way for the development of practical applications. According to the thermodynamic and kinetic uncertainty relations, the precision of currents can be constrained solely by total entropy production or dynamical activity. In this study, we derive a tighter bound on the precision of currents in terms of both thermodynamic and kinetic quantities, demonstrating that these quantities jointly constrain current fluctuations. The thermodynamic and kinetic uncertainty relations become particular cases of our result in asymptotic limits. Intriguingly, the unified thermodynamic-kinetic uncertainty relation leads to a tighter classical speed limit, refining the time constraint on the system's state transformation. The proposed framework can be extended to apply to state observables and systems with unidirectional transitions, thereby providing a constraint on the precision of the first-passage time.

cond-mat.stat-mech↗

arXiv2022

Accelerated Jarzynski Estimator with Deterministic Virtual Trajectories

The Jarzynski estimator is a powerful tool that uses nonequilibrium statistical physics to numerically obtain partition functions of probability distributions. The estimator reconstructs partition functions with trajectories of the simulated Langevin dynamics through the Jarzynski equality. However, the original estimator suffers from slow convergence because it depends on rare trajectories of stochastic dynamics. In this paper, we present a method to significantly accelerate the convergence by introducing deterministic virtual trajectories generated in augmented state space under the Hamiltonian dynamics. We theoretically show that our approach achieves second-order acceleration compared to a naive estimator with the Langevin dynamics and zero variance estimation on harmonic potentials. We also present numerical experiments on three multimodal distributions and a practical example where the proposed method outperforms the conventional method, and provide theoretical explanations.

cond-mat.stat-mech↗

arXiv2022

Thermodynamic uncertainty relation for quantum first passage process

We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains. We consider first passage processes that stop after a fixed number of jumps, which contrasts with typical quantum Markov chains which end at a fixed time. We obtain bounds for the observables of the first passage processes in quantum Markov chains by the Loschmidt echo, which quantifies the extent of irreversibility in quantum many-body systems. Considering a particular case, we show that the lower bound corresponds to the quantum Fisher information, which plays a fundamental role in uncertainty relations in quantum systems. Moreover, considering classical dynamics, our bound reduces to a thermodynamic uncertainty relation for classical first passage processes.

quant-ph↗

arXiv2022

Quantum Walks with Indefinite Causal Order

In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by introducing indefinite causal order ways of coin tossing and investigate this modern scenario. We find that an ideal-shape and fast-spreading uniform distribution can be prepared with our new model. First we will show how an always-symmetrical instantaneous distribution appears in an indefinite causal order quantum walk, which then paves the way for deriving conditions that enables one to interpret an evolved state as a superposition of its definite causal order counterparts which is however in general prohibited. This property of temporal superposition of states can be generalized from two-process scenarios to cases where arbitrary many $\mathcal{N}$ processes are involved. Finally, we demonstrate how a genuine uniform distribution emerges from an indefinite causal order quantum walk. Remarkably, besides the ideal shape of the distribution, our protocol has another powerful advantage, that is the speed of spatial spreading reaches exactly the theoretical limit in contrast to conventional cases where one may encounter the well-known issue of a $1/\sqrt{2}$ degeneration.

quant-ph↗

arXiv2021

Irreversibility, Loschmidt echo, and thermodynamic uncertainty relation

Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed dynamics, our relation leads to several thermodynamic uncertainty relations, indicating that our relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.

cond-mat.stat-mech↗

arXiv2021

Toward relaxation asymmetry: Heating is faster than cooling

An asymmetry in thermal relaxation toward equilibrium has been uncovered for Langevin systems near stable minima [Phys. Rev. Lett. 125, 110602 (2020)]. It has been shown that, given the same degree of nonequilibrium of the initial distributions, relaxation from a lower temperature state (heating) is faster than that from a higher temperature state (cooling). In this study, we elucidate this relaxation asymmetry for discrete-state Markovian systems described by the master equation. We rigorously prove that heating is faster than cooling for arbitrary two-state systems, whereas for systems with more than two distinct energy levels, the relaxation asymmetry is no longer universal. Furthermore, for systems whose energy levels degenerate into two energy states, we find that there exist critical thresholds of the energy gap. Depending on the magnitude of the energy gap, heating can be faster or slower than cooling, irrespective of the transition rates between states. Our results clarify the relaxation asymmetry for discrete-state systems and reveal several hidden features inherent in thermal relaxation.

cond-mat.stat-mech↗

arXiv2021

Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems

We consider thermal relaxation process of a quantum system attached to a single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower-bounded by a relative entropy between the unitarily-evolved state and the final state. The bound characterizes the state discrepancy induced by the non-unitary dynamics, thus reflecting the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian; hence, providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. Our finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.

cond-mat.stat-mech↗

arXiv2021

Indefinite Causal Order in Quantum Batteries

Operations performing on quantum batteries are extended to scenarios where we no longer force the existence of definite causal order of occurrence between distinct processes. In contrast to standard theories, the so called indefinite causal order is found to have the capability of accomplishing tasks that are not possible without it. Specifically, we show how this novel class of resource comes into play in quantum batteries by first, combining two static unitary chargers into a coherently superposed one to fully charge an empty battery even if in the presence of battery's local Hamiltonian. Then we demonstrate for a non-unitary charging protocol, the indefinite causal order version charger yields a charged battery with higher energy over its classical counterpart under any conditions. We also have a finding that runs counter to our intuition which, roughly speaking, has the implication that a relatively less powerful charger guarantees a charged battery with higher energy. Finally, to reduce the cost imposed by a measurement-based protection scheme, indefinite causal order shows its potential to fulfill this goal.

quant-ph↗