arXiv subjects

Jin-Fu Chen

Publications and source records attributed to Jin-Fu Chen.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Nonlinear Imaginary-Time Evolution

Imaginary-time evolution (ITE) is a powerful method for ground-state preparation of a given Hamiltonian. The normalized ITE can be viewed as a gradient flow of the energy expectation value with respect to the Fubini--Study metric. In this work, we propose a generalized nonlinear imaginary-time evolution (NITE) for more general quantum state-preparation tasks. We further present a hardware-efficient variational implementation of NITE and reveal its connection to quantum natural gradient descent. NITE is applied to several subroutine tasks, including variance minimization in variational eigensolvers, probe-state preparation in variational quantum sensing, and excited-state preparation using penalty terms. We prove that NITE achieves a local exponential convergence rate under reasonable assumptions. Our results show that NITE outperforms standard gradient descent and can serve as an efficient optimization method for variational tasks beyond ground-state preparation.

quant-ph↗

arXiv2026

Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities

Multipartite Bell nonlocality provides a device-independent probe of many-body quantum correlations, but its characterization is limited by the rapid growth of the underlying classical and quantum optimization problems. We develop a scalable method for constructing and certifying permutationally invariant Bell inequalities using only one- and two-body correlators. The construction gives families of inequalities with robust quantum violations for general $m$ measurements as the number of parties $N$ becomes large. To improve robustness against noise, we optimize the ratio of the quantum value to the classical bound for these families in the large-$N$ limit. We then certify the resulting quantum violation using semidefinite programming. For the broad class of Bell inequalities studied here, the infinite-$N$ ratios take simple rational values for finite $m$ and converge to $\coth(1)$ as $m\to\infty$. The optimized inequalities efficiently detect many-body Bell nonlocality with collective measurements, with more measurement settings leading to stronger violations.

quant-ph↗

arXiv2026

Extending Covariant Fluctuation Theorems into Quantum Regime through Quasiprobability Approach

The covariant formulation of stochastic thermodynamics requires treating the stochastic work as a 4-vector, posing significant challenges for quantum systems due to the non-commutativity. We introduce a new quasiprobability distribution for the work 4-vector, which combines the Wigner and Margenau-Hill quasiprobabilities. This extends the covariant fluctuation theorems from classical to quantum regime. We illustrate our findings with a scalar field driven by classical particles with a generalized version of trace formula. Our work establishes a quasiprobability approach to studying relativistic quantum thermodynamics in a covariant way.

cond-mat.stat-mech↗

arXiv2025

Optimizing quantum violation for multipartite facet Bell inequalities

Nonlocality shapes quantum correlations, revealed through the violation of Bell inequalities. The intersection of all valid Bell inequalities is the so-called local polytope. In multipartite systems, characterizing the local polytope quickly becomes an intractable task as the system size increases. Optimizing Bell inequalities to maximize the ratio between their quantum value and classical bound is key to understanding multipartite nonlocality. We propose a gradient-based method for this optimization. Numerical results indicate that local maxima of this ratio typically correspond to facet Bell inequalities of the local polytope. This enables an iterative search for tight and robust Bell inequalities. Applied to permutation-invariant scenarios, the method provides tight Bell inequalities with large quantum violations and facilitates experimental certification of Bell correlations without full knowledge of the local polytope. Moreover, analytical results of the maximum ratio are derived in the thermodynamic limit.

quant-ph↗

arXiv2025

Monitored quantum transport: full counting statistics of a quantum Hall interferometer

We generalize the Levitov-Lesovik formula for the probability distribution function of the electron charge transferred through a phase coherent conductor, to include projective measurements that monitor the chiral propagation in quantum Hall edge modes. When applied to an electronic Mach-Zehnder interferometer, the monitoring reduces the visibility of the Aharonov-Bohm conductance oscillations while preserving the binomial form of the counting statistics, thereby removing a fundamental shortcoming of the dephasing-probe model of decoherence.

cond-mat.mes-hall↗

arXiv2025

Thermodynamically Consistent Lindbladians for Quantum Stochastic Thermodynamics

We develop a Lindblad framework for quantum stochastic thermodynamics to study the nonequilibrium thermodynamics of open quantum systems. Our approach adopts the local quantum detailed balance condition, ensuring thermodynamic consistency and leading to a joint fluctuation theorem of quantum work and heat. Instead of solving the full evolution of the density matrix, we employ an effective parametrization to derive the full counting statistics of work and heat and determine the optimal protocols. As an application, we refine the quantum Brownian motion master equation to ensure the quantum detailed balance condition, derive the optimal protocols at different temperatures, and study the work statistics. Our framework provides fundamental insights and practical strategies for optimizing thermodynamic processes in open quantum systems.

quant-ph↗

arXiv2024

Boosting thermalization of classical and quantum many-body systems

Understanding and optimizing the relaxation dynamics of many-body systems is essential both for foundational studies in quantum thermodynamics and for applications such as quantum simulation and quantum computing. Efficient preparation of thermal states of a many-body Hamiltonian is governed by the spectral properties of the associated Lindbladian, in particular its spectral gap, which determines the slowest relaxation rate. In this work, we develop a systematic framework for constructing Lindbladians that prepare thermal states. Our approach reveals a simple relation between the relaxation dynamics at finite and infinite temperatures. The framework is scalable to larger system sizes when implemented using tensor-network methods. We find that efficient thermalization requires that the relaxation dynamics respect the symmetries of the thermal state, which reduces the number of free parameters. By applying gradient-based optimization to the Lindbladians, we enhance the spectral gap and thereby boost thermalization. When applied to both classical and quantum spin models, our method demonstrates a substantial enhancement of the spectral gap. For larger system sizes, our approach provides a variational upper bound and enables a certified lower bound on the minimum relaxation rate.

quant-ph↗

arXiv2024

Spectral Gap Optimization for Enhanced Adiabatic State Preparation

The preparation of non-trivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this letter, we propose an efficient method to adiabatically prepare tensor networks states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNS, through examples of random TNS in one dimension, AKLT, and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors.

quant-ph↗

arXiv2024

Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition

Hysteresis and metastable states are typical features associated with ergodicity breaking in the first-order phase transition. We explore the scaling relations of nonequilibrium thermodynamics in finite-time first-order phase transitions. Using the Curie-Weiss model as an example, for large systems we find the excess work scales as $v^{2/3}$ when the magnetic field is quenched at a finite rate $v$ across the phase transition. We further reveal a crossover in the scaling of the excess work from $v^{2/3}$ to $v$ when downsizing the system. Our study elucidates the interplay between the finite-time dynamics and the finite-size effect, which leads to different scaling behaviors of the excess work with or without ergodicity breaking.

cond-mat.stat-mech↗

arXiv2023

Promoting Fluctuation Theorems into Covariant Forms

The principle of covariance, a cornerstone of modern physics, asserts the equivalence of all inertial frames of reference. Fluctuation theorems, as extensions of the second law of thermodynamics, establish universal connections between irreversibility and fluctuation in terms of stochastic thermodynamic quantities. However, these relations typically assume that both the thermodynamic system and the heat bath are at rest with respect to the observer, thereby failing to satisfy the principle of covariance. In this study, by introducing covariant work and heat that incorporate both energy-related and momentum-related components, we promote fluctuation theorems into covariant forms applicable to moving thermodynamic systems and moving heat baths. We illustrate this framework with two examples: the work statistics of a relativistic stochastic field and the heat statistics of a relativistic Brownian motion. Although our study is carried out in the context of special relativity, the results can be extended to the nonrelativistic limit. Our work combines the principle of covariance and fluctuation theorems into a coherent framework and may have applications in the study of thermodynamics relevant to cosmic microwave background as well as the radiative heat transfer and noncontact friction between relatively moving bodies.

cond-mat.stat-mech↗

arXiv2023

Optimal control theory for maximum power of Brownian heat engines

The pursuit of achieving the maximum power in microscopic thermal engines has gained increasing attention in recent studies of stochastic thermodynamics. We employ the optimal control theory to study the performance of Brownian heat engines and determine the optimal heat-engine cycles in generic damped situation, which were previously known only in the overdamped and the underdamped limits. These optimal cycles include two isothermal processes, two adiabatic processes, and an extra isochoric relaxation process at the upper stiffness constraint. Our results not only interpolate the optimal cycles between the overdamped and the underdamped limits, but also determine the appropriate friction coefficient of the Brownian heat engine to achieve the maximum power. These findings offer valuable insights for the development of high-performance Brownian heat engines in experimental setups.

cond-mat.stat-mech↗

arXiv2023

Exploring quasiprobability approach to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution

In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general approach to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit.

cond-mat.stat-mech↗

arXiv2023

Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultra-violet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

cond-mat.stat-mech↗

arXiv2023

Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs

For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint statistics of work and heat in the situation of multiple heat reservoirs via the Feynman-Kac equation. For a classical Brownian particle in contact with multiple heat reservoirs, we verify the validity of the fluctuation theorems for the joint distribution of work and heat.

cond-mat.stat-mech↗

arXiv2022

Geodesic bound of the minimum energy expense to achieve membrane separation within finite time

To accomplish a task within limited operation time typically requires an excess expense of energy, whose minimum is of practical importance for the optimal design in various applications, especially in the industrial separation of mixtures for purification of components. Technological progress has been made to achieve better purification with lower energy expense, yet little is known about the fundamental limit on the least excess energy expense in finite operation time. We derive such a limit and show its proportionality to the square of a geometric distance between the initial and final states and inverse proportionality to the operation time $τ$. Our result demonstrates that optimizing the separation protocol is equivalent to finding the geodesic curve in a geometric space. Interestingly, we show the optimal control with the minimum energy expense is achieved by a symmetry-breaking protocol, where the two membranes are moved toward each other with different speeds.

math.OC↗

arXiv2022

Optimizing Brownian heat engine with shortcut strategy

Shortcuts to isothermality provide a powerful method to speed up quasistatic thermodynamic processes within finite-time manipulation. We employ the shortcut strategy to design and optimize Brownian heat engines, and formulate a geometric description of the energetics with the thermodynamic length. We obtain a tight and reachable bound of the output power, which is reached by the optimal protocol to vary the control parameters with a proper constant velocity of the thermodynamic length. Our results generalize the previous optimization in the highly underdamped and the overdamped regimes to the general-damped situation, and are applicable for arbitrary finite-time cycles.

cond-mat.stat-mech↗

arXiv2022

Speeding up quantum adiabatic processes with dynamical quantum geometric tensor

For adiabatic controls of quantum systems, the non-adiabatic transitions are reduced by increasing the operation time of processes. Perfect quantum adiabaticity usually requires the infinitely slow variation of control parameters. In this paper, we propose the dynamical quantum geometric tensor, as a metric in the control parameter space, to speed up quantum adiabatic processes and reach quantum adiabaticity in relatively short time. The optimal protocol to reach quantum adiabaticity is to vary the control parameter with a constant velocity along the geodesic path according to the metric. For the system initiated from the n-th eigenstate, the transition probability in the optimal protocol is bounded by P_{n}(t)\leq4\mathcal{L}_{n}^{2}/τ^{2} with the operation time τand the quantum adiabatic length \mathcal{L}_{n} induced by the metric. Our optimization strategy is illustrated via two explicit models, the Landau-Zener model and the one-dimensional transverse Ising model.

quant-ph↗

arXiv2021

Minimal Energy Cost to Initialize a Quantum Bit with Tolerable Error

Landauer's principle imposes a fundamental limit on the energy cost to perfectly initialize a classical bit, which is only reached under the ideal operation with infinite-long time. The question on the cost in the practical operation for a quantum bit (qubit) has been posted under the constraint by the finiteness of operation time. We discover a raise-up of energy cost by $\mathcal{L}^{2}(ε)/τ$ from the Landaeur's limit ($k_{B}T\ln2$) for a finite-time $τ$ initialization with an error probability $ε$. The thermodynamic length $\mathcal{L}(ε)$ between the states before and after initializing in the parametric space increases monotonously as the error decreases. For example, in the constant dissipation coefficient ($γ_{0}$) case, the minimal additional cost is $0.997k_{B}T/(γ_{0}τ)$ for $ε=1\%$ and $1.288k_{B}T/(γ_{0}τ)$ for $ε=0.1\%$. Furthermore, the optimal protocol to reach the bound of minimal energy cost is proposed for the qubit initialization realized via a finite-time isothermal process.

quant-ph↗