arXiv subjects

Kyungtaek Jun

Publications and source records attributed to Kyungtaek Jun.

At least 19 recordsLinked to original sources

arXiv2026

High-Fidelity ROI CT Reconstruction with Limited Quantum Resources via Hybrid Classical-Quantum Refinement

Quantum optimization for computed tomography (CT) reconstruction is constrained by the number of binary variables required for image representation, making direct whole-image quantum reconstruction difficult for large or structurally complex objects. We propose a hybrid region-of-interest (ROI) refinement framework in which a coarse global image is first reconstructed by quantum tomographic reconstruction (QTR) and quantum compressed sensing tomographic reconstruction (QCSTR), filtered backprojection (FBP), or simultaneous algebraic reconstruction technique (SART), and quantum optimization is then applied only to the selected ROI through a residual projection-image formulation. This strategy reduces the effective QUBO size while preserving high-fidelity reconstruction in the target region. Experiments on three discrete phantom samples show that both QTR/QCSTR+QTR/QCSTR and SART+QTR/QCSTR achieve accurate ROI reconstruction for moderate-size cases under a reduced-angle setting. For the largest and most complex sample, the quality of the coarse global estimate becomes critical, and the best result is obtained when a stable classical coarse reconstruction is combined with second-stage ROI-only QTR/QCSTR. Among the tested pipelines, SART+QTR/QCSTR achieves the lowest average ROI RMSE and MAE. The results indicate that the practical advantage of quantum-assisted CT reconstruction lies in reserving quantum optimization for local refinement while using classical reconstruction to stabilize the global background.

quant-ph↗

arXiv2025

Quantum prime factorization algorithms using binary carry propagation

The RSA cryptosystem, which relies on the computational difficulty of prime factorization, faces growing challenges with the advancement of quantum computing. In this study, we propose a quantum annealing based approach to integer factorization using both high order unconstrained binary optimization (HUBO) and constrained quadratic model (CQM) formulations. We begin by modeling binary multiplication with explicit carry propagation, translating this into a HUBO representation and subsequently reducing it to a quadratic unconstrained binary optimization form compatible with current quantum solvers. To address scalability limitations, we implement a CQM approach with constraint relaxation and global product consistency. While the HUBO model successfully factors small semiprimes, it exhibits exponential memory growth, making it impractical for inputs larger than 10 bits. In contrast, the CQM model achieves accurate factorization of semiprimes up to 60 bits including N = 1152921423002469787 demonstrating significantly improved scalability. Experimental results further show that applying global product constraints enhances factorization accuracy and consistency across all tested instances. This work highlights both the promise and current limitations of quantum-assisted factorization and establishes a foundation for evaluating RSA security in the emerging quantum era.

quant-ph↗

arXiv2025

Quantum compressed sensing tomographic reconstruction algorithm

Computed tomography (CT) is a non-destructive technique for observing internal images and has proven highly valuable in medical diagnostics. Recent advances in quantum computing have begun to influence tomographic reconstruction techniques. The quantum tomographic reconstruction algorithm is less affected by artifacts or noise than classical algorithms by using the square function of the difference between pixels obtained by projecting CT images in quantum superposition states and pixels obtained from experimental data. In particular, by using quantum linear systems, a fast quadratic unconstrained binary optimization (QUBO) model formulation for quantum tomographic reconstruction is possible. In this paper, we formulate the QUBO model for quantum compressed sensing tomographic reconstruction, which is a linear combination of the QUBO model for quantum tomographic reconstruction and the QUBO model for total variation in quantum superposition-state CT images. In our experiments, we used sinograms obtained by using the Radon transform of Shepp-Logan images and body CT images. We evaluate the performance of the new algorithm by reconstructing CT images using a hybrid solver with the QUBO model computed from each sinogram. The new algorithm was able to obtain a solution within 5 projection images for 30 by 30 image samples and within 6 projection images for 60 by 60 image samples, reconstructing error-free CT images. We anticipate that quantum compressed sensing tomographic reconstruction algorithms could significantly reduce the total radiation dose when quantum computing performance advances.

quant-ph↗

arXiv2025

Quantum-Assisted Tomographic Image Refinement with Limited Qubits for High-Resolution Imaging

We propose a quantum-assisted reconstruction framework for high-resolution tomographic imaging that significantly reduces both qubit requirements and radiation exposure. Conventional quantum reconstruction methods require solving QUBO (Quadratic Unconstrained Binary Optimization) problems over full-resolution image grids, which limits scalability under current hardware constraints. Our method addresses this by combining sinogram downscaling with region-wise iterative refinement, allowing reconstruction to begin from a reduced-resolution sinogram and image, then progressively upscaled and optimized region by region. Experimental validation on binary and integer-valued Shepp-Logan phantoms demonstrates accurate reconstructions under both dense and sparsely sampled projection conditions using significantly fewer qubits. We observed that nearest-neighbor interpolation may cause edge artifacts that hinder convergence, which can be mitigated by smoother interpolation and Gaussian filtering. Notably, reconstructing a 500 by 500 image from a 50 by 50 initialization demonstrates the potential for up to 90% reduction in projection data, corresponding to a similar reduction in radiation dose. These findings highlight the practicality and scalability of the proposed method for quantum-enhanced tomographic reconstruction, offering a promising direction for low-dose, high-fidelity imaging with current-generation quantum devices.

quant-ph↗

arXiv2025

Quantum Supremacy in Tomographic Imaging: Advances in Quantum Tomography Algorithms

Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of quantum supremacy, which signifies the ability of quantum processors to surpass classical systems in specific tasks. In the context of tomographic image reconstruction, quantum optimization algorithms enable faster processing and clearer imaging than conventional methods. This study further substantiates quantum supremacy by reducing the required projection angles for tomographic reconstruction while enhancing robustness against image artifacts. Notably, our experiments demonstrated that the proposed algorithm accurately reconstructed tomographic images without artifacts, even when up to 50% error was introduced into the sinogram to induce ring artifacts. Furthermore, it achieved precise reconstructions using only 50% of the projection angles from the original sinogram spanning 0° to 180°. These findings highlight the potential of quantum algorithms to revolutionize tomographic imaging by enabling efficient and accurate reconstructions under challenging conditions, paving the way for broader applications in medical imaging, material science, and advanced tomography systems as quantum computing technologies continue to advance.

quant-ph↗

arXiv2024

QUBO Refinement: Achieving Superior Precision through Iterative Quantum Formulation with Limited Qubits

In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical computers. Notably, the hybrid solver provided by the D-wave system can leverage up to two million variables. By exploiting this technology, quantum optimization models based on quadratic unconstrained binary optimization (QUBO) have been proposed for applications, such as linear systems, eigenvalue problems, RSA cryptosystems, and CT image reconstruction. The formulation of QUBO typically involves straightforward arithmetic operations, presenting significant potential for future advancements as quantum computers continue to evolve. A prevalent approach in these developments is the binarization of variables and their mapping to multiple qubits. These methods increase the required number of qubits as the range and precision of each variable increase. Determining the optimal value of a QUBO model becomes more challenging as the number of qubits increases. Furthermore, the accuracies of the existing Qiskit simulator, D-Wave system simulator, and hybrid solver are limited to two decimal places. Problems arise because the qubits yielding the optimal value for the QUBO model may not necessarily correspond to the solution of a given problem. To address these issues, we propose a new iterative algorithm. The novel algorithm sequentially progresses from the highest to the lowest exponent in binarizing each number, whereby each number is calculated using two variables, and the accuracy can be computed up to a maximum of 16 decimal places.

quant-ph↗

arXiv2024

Quantum optimization algorithms for CT image segmentation from X-ray data

Computed tomography (CT) is an important imaging technique used in medical analysis of the internal structure of the human body. Previously, image segmentation methods were required after acquiring reconstructed CT images to obtain segmented CT images which made it susceptible to errors from both reconstruction and segmentation algorithms. However, this paper introduces a new approach using an advanced quantum optimization algorithm called quadratic unconstrained binary optimization (QUBO). This algorithm enables acquisition of segmented CT images from X-ray projection data with minimized discrepancies between experimentally obtained sinograms and quantized sinograms derived from quantized segmented CT images using the Radon transform. This study utilized D-Wave's hybrid solver system for verification on real-world X-ray data.

quant-ph↗

arXiv2023

HUBO and QUBO models for Prime factorization

The security of the RSA cryptosystem is based on the difficulty of factoring a large number N into prime numbers p and q satisfying N=p*q . This paper presents a prime factoriaation method using D-Wave quantum computer that can threaten the RSA cryptosystem. The starting point for this method is very simple, representing two prime numbers as qubits. Then, set the difference between the product of two prime numbers expressed in qubits and N as a cost function, and find the solution when the cost function becomes the minimum. D-Wave's quantum annealer can find the minimum value of any quadratic problem. However, the cost function is to be a higher-order unconstrained optimiaation (HUBO) model because it contains the second or higher order terms. We used a hybrid solver and dimod package provided by -Wave Ocean software development kit (SDK) to solve the HUBO problem. We also successfully factoriaed 102,454,763 with 26 logical qubits. In addition, we factoriaed 1,000,070,001,221 using the range dependent Hamiltonian algorithm.

quant-ph↗

arXiv2022

Highly accurate quantum optimization algorithm for CT image reconstructions based on sinogram patterns

Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts generated during the CT scanning process, along with limitations of back projection algorithms. Recently, an iterative optimization algorithm has been developed that uses the entire sinogram to reduce errors caused by artifacts. In this paper, we introduce a new quantum algorithm for reconstructing CT images. This algorithm can be used with any type of light source as long as the projection is defined. Suppose we have an experimental sinogram produced by a Radon transform. To find the CT image of this sinogram, we express the CT image as a combination of qubits. After the Radon transform of the undetermined CT image, we find the combination of the actual sinogram and the optimized qubits. The global energy optimization value used here can determine the value of qubits through a gate model quantum computer or quantum annealer. In particular, the new algorithm can also be used for cone-beam CT image reconstructions and will be of great help in the field of medical imaging.

quant-ph↗

arXiv2022

Range dependent Hamiltonian Algorithm for numerical QUBO formulation

With the advent and development of quantum computers, various quantum algorithms that can solve linear equations and eigenvalues faster than classical computers have been developed. The Harrow-Hassidim-Lloyd algorithm is an algorithm that can solve linear equations in a gate model quantum computer. Still, it is constrained by the use of quantum RAM and the size limit of the matrix according to the total number of qubits in the quantum computer. Recently, Jun and Lee developed a QUBO model for solving linear systems and eigenvalue problems in the quantum computer. However, even though their model uses 2048 qubits, the number of qubits for variables that can be used for the problem is only 64. To solve this problem, we introduce an algorithm that can be used by dividing the size of the entire domain according to the number of qubits. We also form a QUBO model related to each subregion.

quant-ph↗

arXiv2022

QUBO formulations for numerical quantum computing

With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all science and engineering. The Harrow-Hassidim-Lloyd algorithm, a monumental quantum algorithm for solving linear systems on gate model quantum computers, was invented and several advanced variations have been developed. For a given n by n matrix A and a vector b, we will find unconstrained binary optimization (QUBO) models for a vector x that satisfies Ax=b. To formulate QUBO models for a linear system solving problem, we make use of a linear least-square problem with binary representation of the solution. We validate those QUBO models on the D-Wave system and discuss the results. For a simple system, we provide a Python code to calculate the matrix characterizing the relationship between the variables and to print the test code that can be used directly in the D-Wave system.

quant-ph↗

arXiv2021

On the application of Sylvester's law of inertia to QUBO formulations for systems of linear equations

Previous research on quantum annealing methods focused on effectively modeling systems of linear equations by utilizing quadratic unconstrained binary optimization (QUBO) formulations. These studies take part in enhancing quantum computing algorithms, which extract properties of quantum computers suitable for improving classical computational models. In this paper, we further develop the QUBO formulations of systems of linear equations by applying Sylvester's law of inertia, which explores matrix congruence of any real symmetric matrix to a diagonal matrix. We expect that the proposed algorithm can effectively implement higher dimensional systems of linear equations on a quantum computer. Further experimental verification of the proposed QUBO models as well as their comparisons to classical algorithms are also made.

quant-ph↗

arXiv2021

Noise-resistant reconstruction algorithm based on the sinogram pattern

We introduce a new CT image reconstruction algorithm that is less affected by various artifacts. The new reconstruction algorithm is a method of minimizing the difference between synchrotron X-ray tomography data and sinograms generated using Radon transform of CT images. The CT image is iteratively updated to reduce the difference from the sinogram of the data. This method can obtain clean CT images from the projection data, which can create ring artifacts or metal artifacts. Also, even if the sample size is larger than the CCD and/or the projection image does not satisfy the Beer-Lambert law, a clean CT image can be reconstructed. Our new reconstruction algorithm can also be applied to fan beam CT or cone beam CT

physics.med-ph↗

arXiv2021

On the application of matrix congruence to QUBO formulations for systems of linear equations

Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively parallelize quadratic unconstrained binary optimization (QUBO) formulations of systems of linear equations. In this paper, we simplify these formulations by exploiting congruence of real symmetric matrices to diagonal matrices. We further exhibit computational merits of the proposed QUBO models, which can outperform classical algorithms such as QR and SVD decomposition.

quant-ph↗

arXiv2020

Virtual Alignment Method and its application to the dental prostheses and diagnosis

The recent proposal of a new alignment solution for X-ray tomography, Virtual alignment method (VAM) allowed a more accurate method to remove the possible errors that limit the resolution and clarity of the reconstructed image. In the field of dentistry, the movement of patients during the scanning poses as one of the major factors hindering the final reconstructed image quality. Here, the patient's movement was artificially given to the projection image set and the newly proposed algorithm using the sinogram and the fixed point was applied to the tooth sample to compare the reconstruction image to the actual projection image set. The new alignment method showed promising results by reducing the margin of errors down to a few micrometer, which will allow the production of high-quality dental prostheses with accuracy and precision. We hope that the newly proposed alignment method can be further investigated to be applied more readily in the filed of dentistry ot provide better quality images of patients to make a more accurate diagnosis and prostheses.

eess.IV↗

arXiv2020

Possibility of using Parallel beam CT in dental treatment by correction of movement errors with virtual Alignment Method

The purpose of this study is to correct the movement errors that may occur because of the patients' movement during the CT scanning and thus, to obtain more precise CT images, additionally to investigate the possible use of Parallel Beam CT in the dental treatment. An extracted human tooth was scanned with PBCT and the possible movement errors that patients may cause during the CT scan were intentionally assigned. The maximum width of errors was designed to reach 0.1 mm. The trajectory of the fixed point was traced in the sinogram that includes the fixed point. The part deviated from the sinusoidal curve was modified using the Virtual Alignment Method. The quality of reconstructed image was remarkably degraded when the movement errors were given. A radiopaque part inside the tooth was used as a fixed point. The errors were corrected by shifting the fixed point to the center of sinogram and this relocation of fixed point did not cause any distortion of image or change of size. The movement errors were corrected with the fixed point inside the tooth. The more precise CT images obtained through this method are expected to be of extensive application in the area of dental treatment using CAD/CAM.

physics.med-ph↗

arXiv2017

Alignment Theory of Parallel-beam CT Image Reconstruction for Elastic-type Objects using Virtual Focusing Method

X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of projected images from an object showing elastic motion. Here, we present a mathematical solution to reconstruct the projection image set obtained from an object with specific elastic motions: periodically, regularly, and elliptically expanded or contracted specimens. To reconstruct the projection image set from expanded or contracted specimens, we introduce new methods; detection of sample's motion modes, mathematical re-scaling pixel values and converting projection angle for a common layer

physics.comp-ph↗

arXiv2017

Alignment Methods and Analysis of Tilt Angle Range for the Data Scanned in Electron Tomography

Electron tomography has been studied in various fields. Various methods have been developed to align projection sets to construct ideally focused reconstruction. In this paper, we present how to align the projection set to distinguish whether it has an ideal sinogram pattern or not by removing translation errors and vertical tilt errors. We also analyze some important properties for certain types of samples to identify whether the reconstruction image can be made through an ideal sinogram pattern. We provide a guideline for how to construct a better reconstruction image by scanning the sample through these properties.

physics.med-ph↗