Quantum Supremacy in Tomographic Imaging: Advances in Quantum Tomography Algorithms

Hyunju Lee; Kyungtaek Jun

REVIEW 5 major objections 5 minor 28 references

Quantum Supremacy in Tomographic Imaging: Advances in Quantum Tomography Algorithms

T0 review · 5 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that a QUBO-based quantum annealing algorithm reconstructs tomograms exactly, with mean absolute error zero, even when half the sinogram is corrupted or half the projection angles are missing, while classical FFT and…

desk verdict An honest, reproducible extension of the authors' own QUBO tomography framework, but the 'quantum supremacy' conclusion is unsupported because the classical baselines are not run on the same masked problem. read the letter →

arxiv 2502.04830 v1 pith:I65W7LNW submitted 2025-02-07 quant-ph eess.IV

Hyunju Lee , Kyungtaek Jun This is my paper · ORCID

classification quant-pheess.IV

keywords quantumtomographyQUBOannealingtomographicimagereconstructionringartifactslimited-anglemissingwedgesupremacy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that tomographic image reconstruction can be written as a quadratic unconstrained binary optimization (QUBO) problem and solved by a quantum-annealing hybrid solver so accurately that the reconstructed image matches the original pixel for pixel. In its tabulated experiments the method reports mean absolute error (MAE) 0 for a 50 × 50 body CT image even when half of the sinogram rows carry injected ring-artifact errors and when half of the projection angles are missing, while FFT, a commercial mathematical solver, and simulated annealing produce nonzero errors or no solution on the same cases. The paper calls this quantum supremacy in tomographic imaging. It also reports cases where the solver misses the global minimum, notably a 100 × 100 tooth reconstruction and a 30 × 30 head image at 20 percent error, so the exactness claim is tied to the tested instances. If the claim holds, the approach would make limited-angle and artifact-heavy reconstructions practical in medical imaging and electron tomography.

What carries the argument

The load-bearing object is the error-excluded QUBO cost function, Eq. (17): $\sum_{(\theta,s)\in D\setminus E} \{(I_P - P)(\theta,s)\}^2 - \sum_{(\theta,s)\in D\setminus E} \{P(\theta,s)\}^2$, where $P$ is the measured sinogram, $I_P$ is the Radon transform of a candidate binary-encoded image, $D$ is the full sinogram domain, and $E$ is the detected error region. Pixel values are expanded as weighted sums of binary qubits, for example $I_{ij} = \alpha_1 + \sum_k (\alpha_k - \alpha_{k-1}) q_k^{ij}$, so the squared mismatch becomes linear and quadratic in the binary variables. The error region $E$ is found by thresholding the mean absolute density difference between adjacent pixels along the position axis, and the reduced QUBO is handed to a hybrid quantum annealer. The exactness claim is carried by the solver reaching a global minimum whose objective value matches the theoretical minimum $-\sum_{D\setminus E} \{P(\theta,s)\}^2$, giving MAE 0.

What would settle it

Run the proposed method on a real sinogram from a CT scan with a known detector defect, keeping clinical image sizes, and compare against a defect-free reference; if the density-variation detector fails to isolate the defective rows or the solver returns MAE greater than zero, the central claim fails. A simpler check is to repeat the 50-percent-missing-angle experiment on the 50 × 50 body image with a new random seed and verify MAE 0; the paper already reports the solver missing the global minimum for the 100 × 100 tooth case, so that experiment directly tests the claimed robustness.

Watch

Extended reading notes

Core claim

The central claim is that excluding corrupted regions of a sinogram before building the QUBO objective lets a quantum annealer find a global minimum that classical optimizers miss. The authors encode each pixel of the target image as qubits whose coefficients follow a mass-attenuation representation, define the cost as the sum of squared differences between the measured sinogram and the Radon transform of the candidate image over the uncorrupted domain $D \setminus E$, and solve the resulting binary quadratic model with a hybrid quantum-classical solver. Table I reports MAE 0 for all tested ring-artifact rates (10 to 50 percent) and all tested missing-angle rates (10 to 50 percent) on the 50 × 50 body image, and for the 30 × 30 head image at 10 percent error. The same QUBO given to classical tools either returns nonzero MAE or no solution within the time budget. The authors interpret this as demonstrating quantum supremacy for tomographic reconstruction.

Load-bearing premise

The argument relies on two linked assumptions: that corrupted sinogram rows can be reliably detected by abrupt density changes between neighboring pixels, and that after those rows are removed the remaining QUBO is small enough for the quantum hybrid solver to find the true global minimum.

Editorial extensions

If this is right

CT scanning could tolerate detector miscalibration without re-scanning, because corrupted projection rows are excluded from the objective rather than corrected.
Limited-angle reconstruction from half the angular range would shorten scan times, reduce radiation dose, and address the missing-wedge problem in electron tomography.
The same error-exclusion recipe should transfer to other inverse problems that can be expressed as QUBO cost functions, such as metal-artifact removal by masking high-density pixels.
The paper's own failure cases show the exactness result is sensitive to problem size and solver behavior, so scaling to clinical images will require larger quantum processors or better solvers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper, the method suggests a generic recipe for inverse problems: formulate the objective only on the trustworthy subdomain of the data, which could apply to denoising, deconvolution, and sparse-view reconstruction beyond tomography.
Beyond the paper, the quantum-supremacy claim should be read as benchmark superiority on small constructed instances rather than a complexity-theoretic separation, since the paper compares finite solvers on fixed QUBOs.
Beyond the paper, a testable extension is to calibrate the error-row detector on real detector defects, because the paper uses artificial errors and notes that real defects are washed out during resizing.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read this one for what it is: an incremental but honest extension of the authors' own QUBO tomography framework, wrapped in a claim of quantum supremacy that the experiments do not support. The genuinely new piece is excluding error-affected sinogram rows from the QUBO domain and showing the approach on ring-artifact and limited-angle cases. The method section is clear, the QUBO algebra is standard least squares, and the code is on GitHub. That is real, reproducible work, and the 25-projection Shepp-Logan result with the hybrid solver matching the original is a legitimate data point.

The soft spot is the comparison. The central inference—that MAE 0 from the hybrid solver beats classical methods—rests on baselines that are not credible for the same preprocessing. FFT is a linear filter, not a solver for the masked problem; Gurobi is run only to presolve; SA is the untuned D-Wave sampler. No competent classical discrete-tomography or TV-regularized reconstruction is run on the error-masked sinogram. The 50% error case becomes a limited-data problem from the unmasked rows, exactly where classical methods are strong, so the table shows only that a commercial hybrid QUBO solver beats weak baselines. The paper's own Section V admits the hybrid solver misses the global minimum on the 100x100 tooth and at 20% error for the head image, so the exact MAE 0 is conditional and instance-size dependent.

The error detection threshold is never specified, and the MAE 0 results are fits to the retained sinogram, not predictions against held-out data. That circularity is real but minor if the claim were only 'we can reconstruct from masked sinograms'; it becomes load-bearing because the claim is supremacy.

What the paper does well: it states its limitations plainly, describes preprocessing, and ships code, so the empirical part is checkable. Self-citation is not the problem; the prior QUBO work is real and the extension is clearly framed. I would not reject this as nonsense. I would reject the supremacy conclusion and ask for a proper classical baseline on the masked data, plus a specified detection threshold.

Who this is for: people working on QUBO formulations for tomography, and anyone tracking weak-baseline pitfalls in quantum-advantage claims. It deserves a serious referee because the core experiments are reproducible and the flaw is fixable; the right outcome is major revision or rejection, depending on whether the authors will run the missing control.

Referee Report

5 major / 5 minor

Summary. The paper proposes a QUBO-based formulation for parallel-beam tomographic image reconstruction, solves the resulting binary optimization problems with D-Wave's hybrid solver, and compares against FFT/iradon, Gurobi (presolve only), and D-Wave's simulated-annealing sampler. The central claim is that the quantum/hybrid approach achieves 'quantum supremacy' in tomographic imaging by reconstructing images with MAE 0 from sinograms with up to 50% injected ring-artifact errors and from only 50% of the projection angles. Experiments are reported on Shepp-Logan, tooth, body, and head datasets of sizes 30x30 to 100x100, with pixel value ranges from binary to 0-10.

Significance. If the central claim were supported, exact tomographic reconstruction from half the projection angles and from heavily corrupted sinograms would be a practically interesting result for discrete tomography. The QUBO least-squares expansion in Section II.A is standard and the authors provide a public code repository, which are positive elements. However, the claimed quantum supremacy is not established: the classical baselines are truncated or unrepresentative, the error-detection step is unspecified and likely uses knowledge of the injected artifacts, and the paper itself reports solver suboptimality in key cases. The significance of the work as presented is therefore mostly a proof-of-concept that a commercial hybrid QUBO solver can fit small noiseless masked tomography problems, not a demonstration of quantum advantage.

major comments (5)

[Section III.B and Table I] The Gurobi baseline is not a real classical optimization baseline: the authors state that they 'focused on the solution obtained from the presolve stage' rather than allowing Gurobi to solve the QUBO. Presolve is a preprocessing step, so the Gurobi MAE values in Table I do not represent the capability of a state-of-the-art classical QUBO/MILP solver. A fair comparison requires a complete Gurobi run (or an equivalently strong classical optimizer) on the same instances; without this, the hybrid solver's success cannot be attributed to quantum advantage.
[Section III.C, Eq. (17)] The error-region detection procedure is not specified. The text says errors are detected by examining density variations between adjacent pixels and locating positions 'where pixel values differ markedly,' but no threshold, window size, or algorithmic rule is given, and the red regions in Fig. 2a appear to be selected from knowledge of the injected errors. Because the QUBO is constructed on the masked domain D\E, the entire reconstruction depends on this unspecified step. The method is therefore not reproducible, and the MAE-0 results may be an artifact of excluding exactly the corrupted rows.
[Section IV.B and Section V] The missing control is a competent classical discrete-tomography reconstruction applied to the same masked sinogram. After error exclusion, the task is a noiseless or low-noise integer-valued limited-angle reconstruction, a regime where classical methods such as total-variation-regularized least squares or discrete algebraic reconstruction (DART) are known to be strong. FFT/iradon is a linear filtered-backprojection method, not an optimizer, so its poor performance on masked or limited-angle data is expected and does not demonstrate quantum superiority. A concrete test would be to run a TV-regularized or DART reconstruction on D\E and report the MAE; this is necessary before the Section V claim that the results 'strongly demonstrate the quantum supremacy of our algorithm.'
[Section IV.A.1 and Section V] The paper's own results contradict the claimed robustness. The authors report that the hybrid solver did not reach the global minimum for the 100x100 tooth case (target -5,393,765.588 vs found -5,373,756.428) and failed at 20% error for the head image (target -4,607,247.045 vs found -4,607,144.207). Thus the MAE-0 entries in Table I are instance-dependent and hold only for specific small images and error levels; they do not support a general claim of accurate reconstruction under 'up to 50% error.'
[Table I and Eq. (17)] An MAE of 0 on the masked problem is not, by itself, evidence of quantum supremacy. The QUBO in Eq. (17) is a least-squares fit to the remaining sinogram pixels; since the remaining data are noiseless and the pixel values are small integers, any optimizer that reaches the global minimum of the masked QUBO will recover the original image exactly if the remaining projections determine it. These experiments therefore measure whether the hybrid solver can minimize a specific small QUBO, not whether the reconstruction task is classically intractable. The paper provides no complexity argument or scaling analysis showing that the masked QUBO instances are hard for classical algorithms.

minor comments (5)

[Eq. (17)] The second sum in Eq. (17) appears to be missing the square on P(theta,s); compare with Eq. (10), where the corresponding term is written as {P(theta,s)}^2.
[Section III.A] The parameters of the injected errors are under-specified: the number of corrupted rows, the scaling-factor ranges, and the random seed (if any) are not reported, which hinders reproduction of the ring-artifact experiments in Table I.
[Section IV.A.1] The statement that '50% of the original sinogram data was removed' is not clearly connected to the error-rate definition used elsewhere in the paper; the authors should clarify whether the 50% figure refers to removed projection angles, masked rows, or total sinogram pixels.
[Section II.A, Eq. (4)] With k ranging from 0 to m, the representable integer range is 0 to 2^{m+1}-1, so the phrase 'less than 2^{m+1}' is slightly off; it should be 'at most 2^{m+1}-1.'
[References] Reference [16] contains the typo 'Hubo formulations' instead of 'QUBO formulations,' and reference [18] lists only K. Jun as author although the text attributes the work to 'Jun and Lee.'

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the reconstruction claim is a QUBO data-fit rather than a definitional tautology, though the supremacy comparison rests on weak classical baselines.

full rationale

The paper's central derivation is a QUBO least-squares fit of an image to its sinogram: equation (10) minimizes the squared difference between the simulated sinogram IP and the measured sinogram P, and the true image is a global minimizer because P is generated from that image. This is the standard structure of tomographic reconstruction, not a circular derivation: the image is not an input to the objective, only the sinogram is. The new step in Section III.C excludes an estimated error region E from the QUBO domain; this is a preprocessing choice, and the paper explicitly notes that the excluded rows are the ones that cause ring artifacts. Excluding corrupted measurements and then reconstructing from the remainder is a legitimate robust-reconstruction strategy, and the MAE-0 results depend on the D-Wave hybrid solver actually finding the global minimum, which the paper honestly reports it failed to do in the 100x100 tooth case and for the head image at 20% error. The QUBO formulation is attributed to the authors' prior work [17], [18], but the equations are re-derived in Section II, so the argument does not reduce to a self-citation chain. The main weakness is not circularity but experimental design: Gurobi is run only to presolve, SA is an untuned sampler, and FFT is applied to zero-masked sinograms rather than to the same error-excluded objective, so the 'quantum supremacy' claim is not supported against competent classical reconstruction. These are correctness and comparison concerns, not definitional circularity.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on five free choices and six background assumptions. The most consequential free choice is the unspecified error-region detection threshold; the most consequential assumption is that the D-Wave hybrid solver returns a near-global solution that coincides with the true image. The paper's own Section V limits (solver suboptimality, qubit count) are treated as evidence about these assumptions.

free parameters (4)

Error-region detection threshold
Section III.C describes detecting rows where pixel values 'differ markedly' but gives no quantitative criterion; all results depend on correct identification of E.
Zero-padding width = 11, 10, 5 pixels depending on dataset
Zero-padding is added to Shepp-Logan, Body, and Head images; it provides known background constraints that make the limited-angle QUBO easier to solve, but the widths are chosen by hand.
Pixel value range and qubit encoding = 0-1 tooth, 0-3 body, 0-10 head
The integer range and the qubit representation (Eq. 16) are chosen per dataset, not derived from the physics; this bounds the QUBO search space and affects whether a unique solution exists.
Artificial error scaling factors = random factors, unspecified
The injected errors are generated with random multipliers; without a seed the exact test set is not reproducible, and the chosen factors affect the difficulty of the reconstruction.

assumptions (6)

domain assumption The Radon transform model P(theta,s) = integral of MAC along ray (Eq. 3) accurately describes the measured sinogram.
All reconstruction targets are defined through this forward model; if the true imaging physics deviates (beam hardening, scatter), the QUBO objective is misspecified.
domain assumption The QUBO formulation from prior work [17,18] correctly encodes tomographic reconstruction as minimization of squared sinogram error.
Sections II.A and II.B restate the authors' earlier derivations; the present work imports them without independent verification.
domain assumption Error-affected regions in the sinogram are horizontal strips that can be identified by density variation and safely excluded.
Section III.C states this; if errors are not localized rows or if exclusion removes essential projection information, the reconstruction is biased or underdetermined.
domain assumption The D-Wave hybrid solver returns a solution close enough to the global QUBO minimum to recover the true image.
The paper concedes the solver missed the global minimum in the tooth case and failed at 20 percent head error; the MAE 0 results depend on this solver assumption.
domain assumption An image with small integer pixel values and known zero-padding can represent the true object.
All test images are resized and quantized to 0-1, 0-3, or 0-10; real clinical images are not binary or low-range integers.
standard math For binary variables q, q^2=q and the QUBO expansion is valid.
Used in Eq. 9 to convert the squared sinogram error into linear and quadratic terms.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Quantum Supremacy in Tomographic Imaging: Advances in Quantum Tomography Algorithms." pith.science (2026). https://pith.science/paper/I65W7LNW

@misc{pith2026250204830,
  author       = {Pith},
  title        = {Pith review of: Quantum Supremacy in Tomographic Imaging: Advances in Quantum Tomography Algorithms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I65W7LNW}},
  note         = {Machine review of arXiv:2502.04830}
}

read the original abstract

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{\deg} to 180{\deg}. 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.

Figures

Figures reproduced from arXiv: 2502.04830 by the authors.

**Figure 1.** Sinograms and corresponding tomographic images for the four datasets used in the experiments. Column 1: High-resolution tomographic images. Column 2: Low-resolution tomographic images derived from the first column. Column 3: The sinogram corresponding to the low-resolution tomographic images used in the experiment. The sinogram preparation method used in our algorithm is consistent across all datasets except for the… view at source ↗

**Figure 3.** Tomographic images reconstructed from the sinogram in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 5.** Experimental results on limited angles for a [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

Figures from the paper (4 more)

**Figure 6.** Figure 6: These horizontal strip errors, which are perpendicular to the position axis, result in circular artifacts when the tomographic image is reconstructed using FFT. As shown in the second column of [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 8.** Figure 8: For the 10% error case, Gurobi, SA, and the hybrid solver all successfully found the correct solution. To evaluate the FFT results using the iradon function, we excluded portions of the sinogram and projection angles containing errors. The FFTreconstructed image was t…

**Figure 6.** Figure 6: Sinograms with different error rates, leading to ring artifacts, and the corresponding tomographic images reconstructed using four methods: FFT, Gurobi, SA, and the Hybrid Solver. TABLE I SUMMARY OF EXPERIMENTAL PARAMETERS AND RESULTS, INCLUDING THE IMAGE SIZE, PIXEL V…

**Figure 7.** Figure 7: Head tomographic image reconstruction results and the corresponding sinograms using four methods: FFT, Gurobi, SA, and Hybrid Solver. The sinogram without errors and its corresponding reconstructed tomographic image are shown in Fig. 1l and Fig. 1k, respectively. As sh…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 26 canonical work pages

[1]

Quantum computing and the entanglement frontier

J. Preskill, “Quantum computing and the entanglement frontier.” 2012

work page 2012
[2]

Polynomial -time algorithms for prime factorization and discrete logarithms on a quantum computer,

P. W. Shor, “Polynomial -time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM review, vol. 41, no. 2, pp. 303 –332, 1999

work page 1999
[3]

The computational complexity of linear optics,

S. Aaronson and A. Arkhipov, “The computational complexity of linear optics,” in Proceedings of the forty-third annual ACM symposium on Theory of computing, 2011, pp. 333–342

work page 2011
[4]

Characterizing quantum supremacy in near- term devices,

S. Boixo, S. V Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven, “Characterizing quantum supremacy in near- term devices,” Nat Phys, vol. 14, no. 6, pp. 595 –600, 2018

work page 2018
[5]

On the complexity and verification of quantum random circuit sampling,

A. Bouland, B. Fefferman, C. Nirkhe, and U. Vazirani, “On the complexity and verification of quantum random circuit sampling,” Nat Phys, vol. 15, no. 2, pp. 159–163, 2019

work page 2019
[6]

Quantum supremacy through the quantum approximate optimization algorithm,

E. Farhi and A. W. Harrow, “Quantum supremacy through the quantum approximate optimization algorithm,” arXiv preprint arXiv:1602.07674, 2016

arXiv 2016
[7]

Quantum supremacy using a programmable superconducting processor,

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, and others, “Quantum supremacy using a programmable superconducting processor,” Nature, vol. 574, no. 7779, pp. 505–510, 2019

work page 2019
[8]

Hartree-Fock on a superconducting qubit quantum computer,

G. A. I. Quantum, Collaborators*†, F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, S. Boixo, M. Broughton, B. B. Buckley, and others, “Hartree-Fock on a superconducting qubit quantum computer,” Science (1979) , vol. 369, no. 6507, pp. 1084–1089, 2020

work page 1979

Show all 28 references

[9]

Quantum shuttle: traffic navigation with quantum computing,

S. Yarkoni, F. Neukart, E. M. G. Tagle, N. Magiera, B. Mehta, K. Hire, S. Narkhede, and M. Hofmann, “Quantum shuttle: traffic navigation with quantum computing,” in Proceedings of the 1st ACM SIGSOFT International Workshop on Architectures and Paradigms for Engineering Quantum...

2020
[10]

Quantum k - nearest neighbors algorithm,

A. Basheer, A. Afham, and S. K. Goyal, “Quantum k - nearest neighbors algorithm,” arXiv preprint arXiv:2003.09187, 2020

2003 arXiv
[11]

Improved financial forecasting via quantum machine learning,

S. Thakkar, S. Kazdaghli, N. Mathur, I. Kerenidis, A. J. Ferreira–Martins, and S. Brito, “Improved financial forecasting via quantum machine learning,” Quantum Mach Intell, vol. 6, no. 1, p. 27, 2024

2024
[12]

Quanvolutional neural networks: powering image recognition with quantum circuits,

M. Henderson, S. Shakya, S. Pradhan, and T. Cook, “Quanvolutional neural networks: powering image recognition with quantum circuits,” Quantum Mach Intell, vol. 2, no. 1, p. 2, 2020

2020
[13]

Shor’s factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers,

E. Gerjuoy, “Shor’s factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers,” Am J Phys, vol. 73, no. 6, pp. 521–540, 2005

2005
[14]

Option pricing using quantum computers,

N. Stamatopoulos, D. J. Egger, Y. Sun, C. Zoufal, R. Iten, N. Shen, and S. Woerner, “Option pricing using quantum computers,” Quantum, vol. 4, p. 291, 2020

2020
[15]

QUBO formulations for a system of linear equations,

K. Jun, “QUBO formulations for a system of linear equations,” Results in Contr ol and Optimization , vol. 14, p. 100380, 2024

2024
[16]

Hubo formulations for solving the eigenvalue problem,

K. Jun and H. Lee, “Hubo formulations for solving the eigenvalue problem,” Results in Control and Optimization, vol. 11, p. 100222, 2023

2023
[17]

A highly accurate quantum optimization algorithm for CT image reconstruction based on sinogram patterns,

K. Jun, “A highly accurate quantum optimization algorithm for CT image reconstruction based on sinogram patterns,” Sci Rep, vol. 13, no. 1, p. 14407, 2023

2023
[18]

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

K. Jun, “Quantum optimization algorithms for CT image segmentation from X -ray data,” arXiv preprint arXiv:2306.05522, 2023

2023 arXiv
[19]

Virtua l multi-alignment theory of parallel-beam CT image reconstruction for elastic objects,

K. Jun and J. Jung, “Virtua l multi-alignment theory of parallel-beam CT image reconstruction for elastic objects,” Sci Rep, vol. 9, no. 1, p. 6847, 2019

2019
[20]

Virtual multi -alignment theory of parallel - beam CT image reconstruction for rigid objects,

K. Jun, “Virtual multi -alignment theory of parallel - beam CT image reconstruction for rigid objects,” Sci Rep, vol. 9, no. 1, pp. 1–9, 2019

2019
[21]

Alignment theory of parallel-beam computed tomography image reconstruction for elastic- type objects using virtual focusing method,

K. Jun and D. Kim, “Alignment theory of parallel-beam computed tomography image reconstruction for elastic- type objects using virtual focusing method,” PLoS One, vol. 13, no. 6, p. e0198259, 2018

2018
[22]

Alignment solution for CT image reconstruction using fixed point and virtual rotation axis,

K. Jun and S. Yoon, “Alignment solution for CT image reconstruction using fixed point and virtual rotation axis,” Sci Rep, vol. 7, no. 1, p. 41218, 2017

2017
[23]

Electron tomography: a three -dimensional analytic tool for hard and soft materials research,

P. Ercius, O. Alaidi, M. J. Rames, and G. Ren, “Electron tomography: a three -dimensional analytic tool for hard and soft materials research,” Advanced materials, vol. 27, no. 38, pp. 5638–5663, 2015

2015
[24]

Photon mass attenuation and energy - absorption coefficients,

J. H. Hubbell, “Photon mass attenuation and energy - absorption coefficients,” Int J Appl Radiat Isot, vol. 33, no. 11, pp. 1269–1290, 1982

1982
[25]

Radiology Data from The Cancer Genome Atlas Lung Adenocarcinoma [TCGA - LUAD] collection

B. Albertina, M. Watson, C. Holback, R. Jarosz, S. Kirk, Y. Lee, and J. Lemmerman, “Radiology Data from The Cancer Genome Atlas Lung Adenocarcinoma [TCGA - LUAD] collection.” The Cancer Imaging Archive, 2016

2016
[26]

Computed Tomography (CT) of the Brain

TrainingDataPro, “Computed Tomography (CT) of the Brain.” 2023

2023
[27]

Cubic -spline interpolation for sparse -view ct image reconstruction with filtered backprojection in dynamic myocardial perfusion imaging,

E. Enjilela, T. -Y. Lee, G. Wisenberg, P. Teefy, R. Bagur, A. Islam, J. Hsieh, and A. So, “Cubic -spline interpolation for sparse -view ct image reconstruction with filtered backprojection in dynamic myocardial perfusion imaging,” Tomography, vol. 5, no. 3, p. 300, 2019

2019
[28]

A deep learning method for simultaneous denoising and missing wedge reconstruction in cryogenic electron tomography,

S. Wiedemann and R. Heckel, “A deep learning method for simultaneous denoising and missing wedge reconstruction in cryogenic electron tomography,” Nat Commun, vol. 15, no. 1, p. 8255, 2024

2024

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

Quantum computing and the entanglement frontier

J. Preskill, “Quantum computing and the entanglement frontier.” 2012

work page 2012

[2] [2]

Polynomial -time algorithms for prime factorization and discrete logarithms on a quantum computer,

P. W. Shor, “Polynomial -time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM review, vol. 41, no. 2, pp. 303 –332, 1999

work page 1999

[3] [3]

The computational complexity of linear optics,

S. Aaronson and A. Arkhipov, “The computational complexity of linear optics,” in Proceedings of the forty-third annual ACM symposium on Theory of computing, 2011, pp. 333–342

work page 2011

[4] [4]

Characterizing quantum supremacy in near- term devices,

S. Boixo, S. V Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding, Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven, “Characterizing quantum supremacy in near- term devices,” Nat Phys, vol. 14, no. 6, pp. 595 –600, 2018

work page 2018

[5] [5]

On the complexity and verification of quantum random circuit sampling,

A. Bouland, B. Fefferman, C. Nirkhe, and U. Vazirani, “On the complexity and verification of quantum random circuit sampling,” Nat Phys, vol. 15, no. 2, pp. 159–163, 2019

work page 2019

[6] [6]

Quantum supremacy through the quantum approximate optimization algorithm,

E. Farhi and A. W. Harrow, “Quantum supremacy through the quantum approximate optimization algorithm,” arXiv preprint arXiv:1602.07674, 2016

arXiv 2016

[7] [7]

Quantum supremacy using a programmable superconducting processor,

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, and others, “Quantum supremacy using a programmable superconducting processor,” Nature, vol. 574, no. 7779, pp. 505–510, 2019

work page 2019

[8] [8]

Hartree-Fock on a superconducting qubit quantum computer,

G. A. I. Quantum, Collaborators*†, F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, S. Boixo, M. Broughton, B. B. Buckley, and others, “Hartree-Fock on a superconducting qubit quantum computer,” Science (1979) , vol. 369, no. 6507, pp. 1084–1089, 2020

work page 1979