Abstract Objective . Despite recent advancements in quantum computing, the limited number of available qubits has hindered progress in CT reconstruction. This study investigates the feasibility of utilizing quantum annealing-based computed tomography (QACT) with current quantum bit levels. Approach . The QACT algorithm aims to precisely solve quadratic unconstrained binary optimization problems. Furthermore, a novel approach is proposed to reconstruct images by approximating real numbers using the variational method. This approach allows for accurate CT image reconstruction using a small number of qubits. The study examines the impact of projection data quantity and noise on various image sizes ranging from 4 × 4 to 24 × 24 pixels. The reconstructed results are compared against conventional reconstruction algorithms, namely maximum likelihood expectation maximization (MLEM) and filtered back projection (FBP). Main result . By employing the variational approach and utilizing two qubits for each pixel of the image, accurate reconstruction was achieved with an adequate number of projections. Under conditions of abundant projections and lower noise levels, the image quality in QACT algorithm outperformed that of MLEM and FBP algorithms. However, in situations with limited projection data and in the presence of noise, the image quality in QACT was inferior to that in MLEM. Significance . This study developed the QACT reconstruction algorithm using the variational approach for real-number reconstruction. Remarkably, only 2 qubits were required for each pixel representation, demonstrating their sufficiency for accurate reconstruction.
Abstract Objective . Despite recent advancements in quantum computing, the limited number of available qubits has hindered progress in CT reconstruction. This study investigates the feasibility of utilizing quantum annealing-based computed tomography (QACT) with current quantum bit levels. Approach . The QACT algorithm aims to precisely solve quadratic unconstrained binary optimization problems. Furthermore, a novel approach is proposed to reconstruct images by approximating real numbers using the variational method. This approach allows for accurate CT image reconstruction using a small number of qubits. The study examines the impact of projection data quantity and noise on various image sizes ranging from 4 × 4 to 24 × 24 pixels. The reconstructed results are compared against conventional reconstruction algorithms, namely maximum likelihood expectation maximization (MLEM) and filtered back projection (FBP). Main result . By employing the variational approach and utilizing two qubits for each pixel of the image, accurate reconstruction was achieved with an adequate number of projections. Under conditions of abundant projections and lower noise levels, the image quality in QACT algorithm outperformed that of MLEM and FBP algorithms. However, in situations with limited projection data and in the presence of noise, the image quality in QACT was inferior to that in MLEM. Significance . This study developed the QACT reconstruction algorithm using the variational approach for real-number reconstruction. Remarkably, only 2 qubits were required for each pixel representation, demonstrating their sufficiency for accurate reconstruction.
One of the primary difficulties in computed tomography (CT) is reconstructing cross-sectional images from measured projections of a physical object. There exist several classical methods for this task of generating a digital representation of the object, including filtered backprojection or simultaneous algebraic reconstruction technique. Our research aims to explore the potential of quantum computing in the field of industrial X-ray transmission tomography. Specifically, this work focuses on the application of a method similar to that proposed by Nau et al. (2023) on real CT data to demonstrate the feasibility of quadratic-unconstrained-binary-optimization-based tomographic reconstruction. Starting with simulated phantoms, results with simulated annealing as well as real annealing hardware are shown, leading to the application on measured cone-beam CT data. The results demonstrate that tomographic reconstruction using quantum annealing is feasible for both simulated and real-world applications. Yet, current limitations—involving the maximum processable size and bit depth of voxel values of the images, both correlated with the number of densely connected qubits within the annealing hardware—imply the need of future research to further improve the results. This approach, despite its early stage, has the potential to enable more sophisticated reconstructions, providing an alternative to traditional classical methods.
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) for CT image segmentation. This algorithm allows CT image reconstruction and segmentation to be performed simultaneously. This algorithm segments CT images by minimizing the difference between a sinogram in a superposition state with qubits, obtained using the mathematical projection including the Radon transform, and the experimentally acquired sinogram from X-ray images for various angles. Furthermore, we leveraged X-ray mass attenuation coefficients to reduce the number of logical qubits required for our quantum optimization algorithm, and we employed D-Wave's hybrid solver to solve the optimization problem. We compared the segmentation results of our algorithm with those of classical algorithms using X-ray images of actual tooth samples to validate the results of our algorithm. The comparison revealed that, after undergoing appropriate image post-processing, our algorithm's segmentation results matched those of classical algorithms that perform segmentation after reconstruction, except for some pixels at the boundary. We expect that the new quantum optimization CT algorithm will bring about great advancements in medical imaging.
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 × 30 image samples and within 6 projection images for 60 × 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.
The emergence of quantum annealers has catalyzed the development of quantum optimization algorithms across various fields. The formulation of a quadratic unconstrained binary optimization (QUBO) model for quantum linear systems suggests that quantum optimization algorithms can play an important role in science and engineering. Recently, a QUBO model was developed by applying a quantum linear system to computed tomography (CT) image reconstruction to clearly show the internal structure of the sample. To date, ultra-clear CT images have not been reconstructed using quantum optimization algorithms owing to limitations in logical qubits. However, the quantum CT image reconstruction algorithm using a quantum linear system provides confidence in the accuracy of the CT image by leveraging the difference between the global and theoretical minimum energies. In this paper, we propose an algorithm that can use two or more QUBO models for CT image reconstruction. The proposed algorithm formulates several QUBO models from CT image reconstruction and verifies them using the hybrid solver of the D-Wave system. The proposed algorithm suggests that quantum-optimized CT algorithms can make greater progress in the future.
Quadratic unconstrained binary optimization (QUBO)-based quantum computed tomography (CT) casts reconstruction as a binary quadratic problem for quantum annealing and hybrid quantum--classical solvers. For grayscale CT, however, image encoding is constrained by the binary-variable budget: fixed global bit-plane encodings increase QUBO size and coupling complexity as gray-level precision improves, whereas low-bit encodings introduce quantization error. We propose a QUBO-based grayscale CT reconstruction framework that combines dynamic interval encoding with prior-balanced optimization. Each refinement round encodes active pixels only within local gray-level intervals around the current estimate, and a boundary-hit-guided update rule adaptively switches between search expansion and local refinement. To improve optimization stability, the method balances projection-domain data consistency and an edge-preserving quadratic prior before forming the final QUBO. Sparse-view and limited-angle fan-beam CT experiments show that the proposed method recovers structures and gray-level distributions more faithfully than the evaluated analytic, iterative, variational, and representation-based baselines. Expressivity analysis and ablation studies further indicate that the improvement mainly arises from effective gray-level representation through dynamic local encoding and more stable data-fidelity--prior coupling. Experiments on the D-Wave hybrid binary quadratic model (BQM) solver further demonstrate that the formulation is executable on a hardware-backed hybrid quantum--classical backend.
Quantum-optimization-based computed tomography (CT) reconstruction has demonstrated quantum supremacy in reconstruction accuracy over conventional classical methods under sparse-view and corrupted-sinogram conditions. However, scaling this approach remains challenging because larger images require increasingly many binary variables and interactions in the underlying quadratic unconstrained binary optimization (QUBO) model. Even with iterative region-of-interest (ROI) refinement, a 60 by 60 ROI with three X-ray mass attenuation coefficients requires 10,800 binary variables under our encoding. As an initial step toward larger quantum CT images, we investigate simulated annealing (SA) followed by spin-error mitigation for optimisation (SEMO), without altering the CT-QUBO objective. We evaluate three 54-view ROI reconstruction instances and nine-view reconstruction with detector-row corruption, comparing SA and SEMO with selected hybrid quantum-classical solver results. For the ROI cases, SEMO reduced the numbers of incorrectly reconstructed pixels in low-budget SA outputs from 13 to 1, 38 to 0, and 54 to 15. With 20 percent detector-row corruption, three of four selected SA and SEMO pairs achieved exact reconstruction. Applying SEMO to one hybrid-solver output reduced its ROI error from 78 to 1 pixel. Improvements were instance-dependent: in one corrupted-sinogram case, QUBO energy decreased while image-domain error increased slightly; in one ROI case, the refined image retained 15 incorrect pixels despite having lower QUBO energy than ground truth. At the evaluated problem sizes, SA and SEMO attained reconstruction accuracy comparable to or better than selected unmitigated hybrid-solver results, providing an initial solution-quality benchmark for future larger-scale, parallelized quantum CT image reconstruction.