arXiv subjects

Katsuhiro Endo

Publications and source records attributed to Katsuhiro Endo.

18 recordsLinked to original sources

arXiv2026

Auto-WHATMD : Automated Wasserstein-based High-dimensional feature extraction Analysis of Trajectories from Molecular Dynamics

Comparing multiple protein systems with variation such as different binding ligands or mutations, and understanding their effects is one of the objectives in molecular dynamics simulations. Representation of these systems by a few features enables quantitative comparison. However, because molecular dynamics simulation trajectories are high-dimensional spatiotemporal data, selection of key features relies on domain expertise, sometimes introducing arbitrary assumptions. Here, we present an approach that uses the optimal transport distance to compare high-dimensional trajectory data, and employs simulated annealing to identify the residues that best distinguish multiple systems. We term this algorithm auto-WHATMD (automated Wasserstein-based High-dimensional feature extraction Analysis for Trajectories of Molecular Dynamics). We applied auto-WHATMD to multiple protein-ligand systems of bromodomain 4 with different ligands, identifying the most discriminative residues in the loop region. Moreover, even a few selected residues were sufficient to capture the correlation with ligand-binding affinities, indicating that auto-WHATMD effectively prioritizes the most informative residues. Our approach can be used to efficiently determine key residues and design features for multiple analogous systems.

physics.chem-ph↗

arXiv2025

Quantum Gradient Flow Algorithm for Symmetric Positive Definite Systems via Quantum Eigenvalue Transformation: Towards Quantum CAE

In this study, we propose the Quantum Gradient Flow Algorithm (QGFA), a novel quantum algorithm for solving symmetric positive definite (SPD) linear systems based on the variational formulation and time-evolution dynamics. Conventional quantum linear solvers, such as the quantum matrix inverse algorithm (QMIA), focus on approximating the matrix inverse through quantum signal processing (QSP). However, QMIA suffers from a crucial drawback: its computational efficiency deteriorates as the condition number increases. In contrast, classical SPD linear solvers, such as the steepest descent and conjugate gradient methods, are known for their fast convergence, which stems from the variational optimization principle of SPD systems. Inspired by this, we develop QGFA, which obtains the solution vector through the gradient-flow process of the corresponding quadratic energy functional. To validate the proposed method, we apply QGFA to the displacement-based finite element method (FEM) for two-dimensional linear elastic problems under plane stress conditions. The algorithm demonstrates accurate convergence toward classical FEM solutions even with a moderate number of QSP phase factors. Compared with QMIA, QGFA achieves lower relative errors and faster convergence when initialized with suitable initial states, demonstrating its potential as an efficient preconditioned quantum linear solver. The proposed framework provides a physically interpretable connection between classical iterative solvers and quantum computational paradigms. These findings suggest that QGFA can serve as a foundation for future developments in Quantum Computer-Aided Engineering (Quantum CAE), including nonlinear and multiphysics simulations.

quant-ph↗

arXiv2025

Quantum-Accelerated Solution of Nonlinear Equations from Variational Principles

Nonlinear equilibrium problems derived from variational principles arise throughout physics and engineering, including structural mechanics, fluid dynamics, and electromagnetism. While fault-tolerant quantum algorithms have shown promising advantages for linear systems and linear dynamical simulations, extending quantum acceleration to nonlinear equilibrium problems remains a major challenge. Here we introduce a quantum algorithmic framework for nonlinear equilibrium analysis based on gradient-flow linearization. The key idea is to reformulate equilibrium conditions as nonlinear gradient-flow dynamics and transform the resulting evolution into a linear dynamical system using exact linearization techniques such as Carleman and Pivot Switching Carleman (PSC) linearization. This construction enables nonlinear equilibrium and energy-minimization problems to be addressed using quantum algorithms for linear dynamical simulation. We demonstrate the framework for nonlinear elasticity problems ranging from single nonlinear springs and chain-spring systems to two-dimensional truss structures. The resulting truncated linearized dynamics accurately reproduce nonlinear equilibrium states, while PSC linearization substantially improves stability in regimes where conventional Carleman linearization becomes unreliable. More broadly, our work establishes a connection between variational principles, nonlinear energy minimization, exact linearization, and quantum dynamical simulation. This perspective opens a route toward quantum algorithms for nonlinear physical systems beyond the scope of existing linear-system-based approaches.

quant-ph↗

arXiv2025

Hamiltonian simulation for nonlinear partial differential equation by Schr\"{o}dingerization

Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup through Hamiltonian simulation has been rigorously demonstrated in the case of coupled harmonic oscillators. The question arises as to whether Hamiltonian simulations in other physical systems also accelerate exponentially. Schr\"odingerization is a technique that transforms the governing equations of classical systems into the Schr\"odinger equation. However, since the Schr\"odinger equation is a linear equation, Hamiltonian simulation is often limited to linear equations. The research on Hamiltonian simulation methods for nonlinear governing equations remains relatively limited. In this study, we propose a Hamiltonian simulation method for nonlinear partial differential equations (PDEs). The proposed method is named Carleman linearization + Schr\"odingerization (CLS), which combines Carleman linearization (CL) and warped phase transformation (WPT). CL is first applied to transform a nonlinear PDE into a linear differential equation. This linearized equation is then mapped to the Schr\"odinger equation via WPT. The original nonlinear PDE can be solved efficiently by the Hamiltonian simulation of the resulting Schr\"odinger equation. By applying this method, we transform the original governing equation into the Schr\"odinger equation. Solving the transformed Schr\"odinger equation then enables the analysis of the original nonlinear equation. As a specific application, we apply this method to the nonlinear reaction--diffusion equation to demonstrate that Hamiltonian simulations are applicable to nonlinear PDEs.

quant-ph↗

arXiv2025

Navigating Phase Transitions with Path-Finding Algorithms: A Strategic Approach to Replica Exchange Monte Carlo

The replica exchange method is a powerful tool for overcoming slow relaxation in molecular simulations, but its efficiency depends strongly on the choice of the number and interval of replicas and their exchange probabilities. Here, we propose a new optimization scheme based on the Dijkstra algorithm that constructs an optimal exchange path by representing replicas and their exchange probabilities as a graph. Inspired by path-finding techniques widely used in computer science, including applications in game algorithms, our approach ensures that transitions follow a minimum entropy gradient path and effectively speeds up sampling even in systems exhibiting slow relaxation near critical points or phase transition regions. The method provides a systematic way to improve replica exchange efficiency and offers new insights into the control of relaxation dynamics, as demonstrated through applications to the solid-liquid phase transition of the Lennard-Jones bulk system.

cond-mat.stat-mech↗

arXiv2024

Divergence-free algorithms for solving nonlinear differential equations on quantum computers

From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their solutions are difficult to obtain. Based on the expectation of quantum transcendence, quantum algorithms for efficiently solving nonlinear differential equations continue to be developed. However, even the latest promising algorithms have been pointed out to have an evolution time limit. This limit is the theoretically predestined divergence of solutions. We propose algorithms of divergence-free simulation for nonlinear differential equations in quantum computers. For Hamiltonian simulations, a pivot state $\bf{s}$ in the neighborhood of state $\bf{x}$ is introduced. Divergence of the solutions is prevented by moving $\bf{s}$ to a neighborhood of $\bf{x}$ whenever $\bf{x}$ leaves the neighborhood of $\bf{s}$. Since updating $\bf{s}$ is directly related to computational cost, to minimize the number of updates, the nonlinear differential equations are approximated by nonlinear polynomials around $\bf{s}$, which are then Carleman linearized. Hamiltonian simulations of nonlinear differential equations based on several representative models are performed to show that the proposed method breaks through the theoretical evolution time limit. The solution of nonlinear differential equations free from evolution time constraints opens the door to practical applications of quantum computers.

quant-ph↗

arXiv2024

An Ising Machine Formulation for Design Updates in Topology Optimization of Flow Channels

Topology optimization is an essential tool in computational engineering, for example, to improve the design and efficiency of flow channels. At the same time, Ising machines, including digital or quantum annealers, have been used as efficient solvers for combinatorial optimization problems. Beyond combinatorial optimization, recent works have demonstrated applicability to other engineering tasks by tailoring corresponding problem formulations. In this study, we present a novel Ising machine formulation for computing design updates during topology optimization with the goal of minimizing dissipation energy in flow channels. We explore the potential of this approach to improve the efficiency and performance of the optimization process. To this end, we conduct experiments to study the impact of various factors within the novel formulation. Additionally, we compare it to a classical method using the number of optimization steps and the final values of the objective function as indicators of the time intensity of the optimization and the performance of the resulting designs, respectively. Our findings show that the proposed update strategy can accelerate the topology optimization process while producing comparable designs. However, it tends to be less exploratory, which may lead to lower performance of the designs. These results highlight the potential of incorporating Ising formulations for optimization tasks but also show their limitations when used to compute design updates in an iterative optimization process. In conclusion, this work provides an efficient alternative for design updates in topology optimization and enhances the understanding of integrating Ising machine formulations in engineering optimization.

cs.CE↗

arXiv2024

Implementation of spectral methods on Ising machines: toward flow simulations on quantum annealer

We investigate the possibility and current limitations of flow computations using quantum annealers by solving a fundamental flow problem on Ising machines. As a fundamental problem, we consider the one-dimensional advection-diffusion equation. We formulate it in a form suited to Ising machines (i.e., both classical and quantum annealers), perform extensive numerical tests on a classical annealer, and finally test it on an actual quantum annealer. To make it possible to process with an Ising machine, the problem is formulated as a minimization problem of the residual of the governing equation discretized using either the spectral method or the finite difference method. The resulting system equation is then converted to the Quadratic Unconstrained Binary Optimization (QUBO) form though quantization of variables. It is found in the numerical tests using a classical annealer that the spectral method requiring smaller number of variables has a particular merit over the finite difference method because the accuracy deteriorates with the increase of the number of variables. We also found that the computational error varies depending on the condition number of the coefficient matrix. In addition, we extended it to a two-dimensional problem and confirmed its fundamental applicability. From the numerical test using a quantum annealer, however, it turns out that the computation using a quantum annealer is still challenging due largely to the structural difference from the classical annealer, which leaves a number of issues toward its practical use.

physics.flu-dyn↗

arXiv2024

Conditional diffusion model for inverse prediction of process parameters and dendritic microstructures from mechanical properties

In this study, we develop a conditional diffusion model that proposes the optimal process parameters and predicts the microstructure for the desired mechanical properties. In materials development, it is costly to try many samples with different parameters in experiments and numerical simulations. The use of data-driven inverse design method can reduce the cost of materials development. This study develops an inverse analysis model that predicts process parameters and microstructures. This method can be used for any material, but in this study it is applied to polymeric material, which is the matrix resin of carbon fiber reinforced thermoplastics as an example. Matrix resins contain a mixture of dendrites, which are crystalline phases, and amorphous phases even after crystal growth is complete, and it is important to consider the microstructures consisting of the crystalline structure and the remaining amorphous phase to achieve the desired mechanical properties. Typically, the temperature during forming affects the microstructures, which in turn affect the macroscopic mechanical properties. The trained diffusion model can propose not only the processing temperature but also the microstructure when Young's modulus and Poisson's ratio are given. The capability of our conditional diffusion model to represent complex dendrites is also noteworthy.

cs.CE↗

arXiv2024

Optimizing a parameterized controlled gate using Free Quaternion Selection

In variational quantum algorithms, parameterization is typically applied to single-qubit gates.In this study, we instead parameterize a generalized controlled gate and propose an algorithm to locally minimize the cost function by maximally optimizing these parameters. This method extends the Free Quaternion Selection (FQS) technique, which was originally developed for single-qubit gate optimization. To evaluate its performance, we apply the proposed method to a variety of quantum optimization tasks, including the Variational Quantum Eigensolver (VQE) for both Ising and molecular Hamiltonians, fidelity maximization in general variational quantum algorithms (VQAs), and unitary compilation of time evolution operators. Across these applications, our method demonstrates efficient optimization, enhanced expressibility, and the ability to construct shallower circuits compared to existing techniques. Moreover, the method can be generalized to optimize particle-number-conserving gates, which are particularly relevant for quantum chemistry. Leveraging this capability, we further demonstrate that the method achieves superior quantum compilation of molecular time-evolution operators by approximating them with shallower circuits than standard Trotter decomposition.

quant-ph↗

arXiv2024

Function Smoothing Regularization for Precision Factorization Machine Annealing in Continuous Variable Optimization Problems

Solving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of the Hamiltonian function surface obtained by factorization machine (FM) have been overlooked. This study shows that in the widely common case where real numbers are represented by a combination of binary variables, the function surface of the Hamiltonian obtained by FM can be very noisy. This noise interferes with the inherent capabilities of quantum annealing and is likely to be a substantial cause of problems previously considered unsolvable due to the limitations of FMQA performance. The origin of the noise is identified and a simple, general method is proposed to prevent its occurrence. The generalization performance of the proposed method and its ability to solve practical problems is demonstrated.

quant-ph↗

arXiv2023

Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver

Variational Quantum Eigensolver (VQE) is a hybrid algorithm for finding the minimum eigenvalue/vector of a given Hamiltonian by optimizing a parametrized quantum circuit (PQC) using a classical computer. Sequential optimization methods, which are often used in quantum circuit tensor networks, are popular for optimizing the parametrized gates of PQCs. This paper focuses on the case where the components to be optimized are single-qubit gates, in which the analytic optimization of a single-qubit gate is sequentially performed. The analytical solution is given by diagonalization of a matrix whose elements are computed from the expectation values of observables specified by a set of predetermined parameters which we call the parameter configurations. In this study, we first show that the optimization accuracy significantly depends on the choice of parameter configurations due to the statistical errors in the expectation values. We then identify a metric that quantifies the optimization accuracy of a parameter configuration for all possible statistical errors, named configuration overhead/cost or C-cost. We theoretically provide the lower bound of C-cost and show that, for the minimum size of parameter configurations, the lower bound is achieved if and only if the parameter configuration satisfies the so-called equiangular line condition. Finally, we provide numerical experiments demonstrating that the optimal parameter configuration exhibits the best result in several VQE problems. We hope that this general statistical methodology will enhance the efficacy of sequential optimization of PQCs for solving practical problems with near-term quantum devices.

quant-ph↗

arXiv2023

Variational quantum algorithm for generalized eigenvalue problems and its application to the finite element method

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the key problems to handle GEPs is that the memory usage and computational complexity explode as the size of the system of interest grows. This paper aims at extending sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms that iteratively solve the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the GEP as the minimization/maximization problem of the fractional form of the expectations of two Hermitians. We then showed that the fractional objective function can be analytically minimized or maximized with respect to a single-qubit gate by solving a GEP of a 4 $\times$ 4 matrix. Second, we show that a system of linear equations (SLE) characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to important engineering problems formulated with the finite element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method.

quant-ph↗

arXiv2022

Prediction of transport property via machine learning molecular movements

Molecular dynamics (MD) simulations are increasingly being combined with machine learning (ML) to predict material properties. The molecular configurations obtained from MD are represented by multiple features, such as thermodynamic properties, and are used as the ML input. However, to accurately find the input--output patterns, ML requires a sufficiently sized dataset that depends on the complexity of the ML model. Generating such a large dataset from MD simulations is not ideal because of their high computation cost. In this study, we present a simple supervised ML method to predict the transport properties of materials. To simplify the model, an unsupervised ML method obtains an efficient representation of molecular movements. This method was applied to predict the viscosity of lubricant molecules in confinement with shear flow. Furthermore, simplicity facilitates the interpretation of the model to understand the molecular mechanics of viscosity. We revealed two types of molecular mechanisms that contribute to low viscosity.

physics.chem-ph↗

arXiv2022

MD-GAN with multi-particle input: the machine learning of long-time molecular behavior from short-time MD data

MD-GAN is a machine learning-based method that can evolve part of the system at any time step, accelerating the generation of molecular dynamics data. For the accurate prediction of MD-GAN, sufficient information on the dynamics of a part of the system should be included with the training data. Therefore, the selection of the part of the system is important for efficient learning. In a previous study, only one particle (or vector) of each molecule was extracted as part of the system. Therefore, we investigated the effectiveness of adding information from other particles to the learning process. In the experiment of the polyethylene system, when the dynamics of three particles of each molecule were used, the diffusion was successfully predicted using one-third of the time length of the training data, compared to the single-particle input. Surprisingly, the unobserved transition of diffusion in the training data was also predicted using this method.

physics.chem-ph↗

arXiv2021

Ligand-induced protein dynamics differences correlate with protein-ligand binding affinities: An unsupervised deep learning approach

Prediction of protein-ligand binding affinity is a major goal in drug discovery. Generally, free energy gap is calculated between two states (e.g., ligand binding and unbinding). The energy gap implicitly includes the effects of changes in protein dynamics induced by the binding ligand. However, the relationship between protein dynamics and binding affinity remains unclear. Here, we propose a novel method that represents protein behavioral change upon ligand binding with a simple feature that can be used to predict protein-ligand affinity. From unbiased molecular simulation data, an unsupervised deep learning method measures the differences in protein dynamics at a ligand-binding site depending on the bound ligands. A dimension-reduction method extracts a dynamic feature that is strongly correlated to the binding affinities. Moreover, the residues that play important roles in protein-ligand interactions are specified based on their contribution to the differences. These results indicate the potential for dynamics-based drug discovery.

q-bio.BM↗

arXiv2020

Quantum self-learning Monte Carlo with quantum Fourier transform sampler

The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution. This paper provides a new self-learning Monte Carlo method that utilizes a quantum computer to output a proposal distribution. In particular, we show a novel subclass of this general scheme based on the quantum Fourier transform circuit; this sampler is classically simulable while having a certain advantage over conventional methods. The performance of this "quantum inspired" algorithm is demonstrated by some numerical simulations.

quant-ph↗

arXiv2019

Molecular Flow Monte Carlo

In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the ability to quickly generate new and independent trial states. Thus, we introduce a continuous normalizing flow method which can quickly generate independent states for various proposal distributions using a first-order differential equation. We define this continuous normalizing molecular flow approach based on two-body intermolecular interactions to achieve a probability distribution transformation method which yields distributions which have probability densities of zero when molecule pairs are in close proximity; while in all other cases, the probability density is compressed such that it is spatial uniform. This transform provides the proposal distribution which generates no states of extremely high energy. We find that an inverse square flow is applicable as the continuous normalizing molecular flow. Using the transformed distribution, we can perform the Metropolis-Hastings method more efficiently. The high efficiency of the proposed method is demonstrated using simple molecular systems.

physics.comp-ph↗