{"id":"7161c8ac-786a-4199-9479-9f63867f68db","arxiv_id":"2505.11286","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Adding a total-variation penalty to the quantum tomographic QUBO model lets the D-Wave hybrid solver rebuild error-free 60 by 60 phantom and body CT images from about 10 percent of the projections, when the weights and test images are chosen favorably.","lead":"This paper merges a quantum CT reconstruction model with a compressed-sensing smoothness penalty into a single optimization problem, and reports that a D-Wave hybrid solver reconstructs error-free 30 by 30 and 60 by 60 test images from roughly 10 to 20 percent of the usual projection count.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported 'error-free within 5-6 projections' depends on per-image hand-selected weights (a,b) in Eq. 9; without a fixed coefficient rule, the central claim is retrospective, not a predictive algorithm result.","rationale":"The paper's own account makes the coefficient-selection problem explicit, and the reader already flagged hand-tuned (a,b) as part of the fitness concerns. I focus on this as the single most load-bearing issue because it undermines the algorithmic status of the central claim: even if the reported energies and images are internally consistent, the error-free results exist only for coefficient choices selected after seeing the test image. The reader's weakest_assumption emphasized the low-cardinality, blurred, known-MAC nature of the samples; that is related but distinct. My proposed test would settle whether a fixed (a,b) can survive out-of-sample reconstruction. Because the authors disclose the limitation and the remedy is additional validation, the appropriate verdict remains CONDITIONAL: the paper should be accepted only with a fixed coefficient rule and out-of-sample benchmarking. Thus the reader's verdict does not change, though the justification is sharpened.","tokens_in":11051,"tokens_out":4838,"duration_ms":52129,"concrete_test":"Run a leave-one-image-out test: use each subset of three of the four reported samples (30/60 Shepp-Logan and 30/60 body) to select a fixed (a,b), e.g., the pair minimizing mean reconstruction error on those three; then reconstruct the held-out image from the claimed 5 or 6 projections and record whether it is error-free. Repeat for all four held-out images. If no fixed (a,b) rule yields error-free results on all held-out images, the 5-6 projection claim must be restated as conditional on per-image coefficient tuning, not as an algorithm-level capability.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In the key experiments, the coefficients in Q = aQ1 + bQ2 (Eq. 9) are not set by a fixed rule but are tuned per test image. The Results state 'We varied b to obtain optimal CT images' for both 60x60 experiments (Figs. 3 and 6), and the Discussion concedes 'the new algorithm requires different a and b to be combined depending on the type of image, and has not yet found the optimal values for the coefficients.' Since b changes the solution (larger b gives 'more monotonous' images; (a,b)=(1,3) gives a one-pixel error for the 60x60 body sample), the reported error-free reconstructions at 5 or 6 projections are selected outcomes of a small grid search over {1,2,3}, not outputs of a pre-specified algorithm. This interacts with the other idealizations (known X-ray MACs, Gaussian-blurred samples, 1- to 1.6-bit pixels), making the abstract's unconditional claim unsupported. A fixed, principled rule for (a,b) is required before 'the new algorithm was able to reconstruct error-free' can be read as a property of the algorithm rather than of the chosen coefficients.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a QUBO formulation for sparse-view CT reconstruction that linearly combines a data-fidelity term (Q1) and a total-variation term (Q2), with Q = aQ1 + bQ2, solved by D-Wave's hybrid BQM solver. Experiments on 30x30 and 60x60 Shepp-Logan and body CT samples, restricted to 1-3 known X-ray MAC values and Gaussian-blurred to be continuous, report error-free reconstructions with 5-6 projections (10-20% of the conventional count). The paper extrapolates to a potential 90% radiation dose reduction in clinical CT.","tokens_in":11145,"tokens_out":5906,"duration_ms":53180,"significance":"The QUBO algebra in Eqs. (1)-(9) is explicit and the energy values reported are consistent with the known samples, and the supplementary code supports reproducibility. If the hyperparameter issue were resolved, the demonstration would establish a useful proof-of-concept for quantum annealing in sparse-view CT for discrete multi-material objects. However, the significance is currently limited because the central claim is tied to per-image tuned coefficients, a highly idealized sample model, and no classical compressed-sensing baseline, so the practical advantage over existing algorithms is not established.","major_comments":[{"comment":"The central claim of error-free reconstruction with 5-6 projections is not a property of the algorithm as stated, because the coefficients (a,b) in Eq. (9) are selected per image. The Results state 'We varied b to obtain optimal CT images' for the 60x60 experiments (Figs. 3 and 6), and the Discussion concedes 'the new algorithm requires different a and b to be combined depending on the type of image, and has not yet found the optimal values for the coefficients.' Since (a,b)=(1,3) already gives a one-pixel error for the 60x60 body sample, the reported error-free results are outcomes of a small grid search rather than of a pre-specified algorithm. Please provide a fixed rule for choosing (a,b), or explicitly scope the claim to the selected coefficients.","section":"Result and implementation / Discussion"},{"comment":"The experimental setting is far more idealized than the abstract suggests: the objects have 1-3 known discrete MAC values (1-1.6 bits per pixel), the samples are Gaussian-blurred to make interior changes as continuous as possible, and the sinograms are ideal. The Discussion acknowledges that 'if the internal structure of the sample has many discontinuous changes or many fast-changing continuous pixels, more projection images are required,' which directly undermines the abstract's unconditional statement that 'the new algorithm was able to obtain a solution within 5 projection images... reconstructing error-free CT images.' The extrapolation to 1000x1000 clinical CT with 90% dose reduction is unsupported by the present experiments.","section":"Result and implementation / Discussion"},{"comment":"The comparison with classical algorithms is incomplete: SART and FBP are standard baselines, but the paper does not include a classical compressed-sensing reconstruction (e.g., TV-regularized SART or L1 minimization) that would exploit the same known discrete label structure. Without such a baseline, the claim that the QCSTR algorithm 'is less affected by artifacts or noise than classical algorithms' is not demonstrated; the observed success may be due to the strong prior (known labels, smooth image) rather than to the quantum solver.","section":"Comparison of classical and quantum CT images"}],"minor_comments":[{"comment":"The text contains a typo: 'exactly the same evergy' should be 'exactly the same energy'.","section":"Result and implementation B"},{"comment":"The noise model in the paragraph beginning 'We have investigated...' is labeled Eq. (10) in the text but appears as Eq. (9) in the manuscript; renumber the equations accordingly.","section":"Result and implementation (noise experiment)"},{"comment":"In Figure 7, the early QTR algorithm is cited as reference [17], but the quantum tomographic reconstruction algorithm is reference [19]; verify the citation.","section":"Comparison of classical and quantum CT images"},{"comment":"The phrase 'quantum supremacy' is used loosely to describe image quality improvements and is misleading in this context; please replace it with 'quantum advantage' or a more specific statement.","section":"Introduction"},{"comment":"The statement that 'quantum compressed sensing algorithms can be calculated within a few flops through parallel operations' is vague and should be replaced with a precise computational complexity statement or omitted.","section":"Discussion"},{"comment":"The spelling 'Helgason-Ludwing' should be 'Helgason-Ludwig'.","section":"Comparison of classical and quantum CT images"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is an incremental extension of the authors' previous QTR work (Refs. [19,29]), and the novelty beyond the existing QUBO formulations is mostly the linear combination with a total-variation term; the authors should clarify the novelty relative to those earlier papers. The competing interests statement notes that the algorithm is patented, which is acceptable, but the authors should ensure that the code release and the patent do not conflict with the journal's reproducibility requirements."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take on arXiv:2505.11286. What is actually new: the authors add a total-variation term, encoded as a QUBO, to their earlier quantum tomographic reconstruction (QTR) formulation, and minimize Q = aQ1 + bQ2 with D-Wave's hybrid BQM solver. The algebraic expansion in Eqs. 6–8 is straightforward, and they ship Python code. That's real, reproducible work, and it should count.\n\nThe paper also includes an honest limitations section: the coefficients a,b are not known a priori, the noisy sinogram does not reach the global minimum, and more projections are needed for discontinuous structures. Good.\n\nNow the soft spots. The stress-test note is correct and it matters. In the key 60x60 experiments they say 'we varied b to obtain optimal CT images.' So the error-free reconstructions at 5 or 6 projections are selected outcomes of a small grid search over a few integer weights, not the output of a fixed algorithm. The abstract's unconditional 'able to obtain' is not supported. The test images are also easy: three known MAC values, Gaussian-blurred, each pixel carrying at most two bits. This is a toy labeling problem. There is no classical compressed-sensing baseline (TV-minimization) in the sparse-view comparison; the classical algorithms shown are SART and FBP, which are not designed for 10% data. The noise experiment is a single run, so the 'good results' claim has no statistics.\n\nI don't think the paper is wrong in its narrow claims. If you read it as 'on these four images, with hand-tuned weights, the BQM solver finds the global minimum and yields exact or near-exact reconstructions,' that's consistent. But the paper sells it as a general algorithm with a 90% dose reduction. That extrapolation outruns the evidence.\n\nWho is this for? Someone working on QUBO formulations for tomographic reconstruction will find the TV expansion useful, and the code is a service. It deserves a serious referee: the method is clearly described, the math is checkable, and the limitations are mostly disclosed. But I would not accept it as is. Required: a fixed, principled rule for a,b; a proper classical compressed-sensing baseline (e.g., total-variation minimization via ADMM); and tests on continuous-valued, unblurred images with unknown attenuation. With those, the claim would be testable. Send it to review with the expectation of major revision.\n\nWant to discuss over coffee?","headline":"A transparent, reproducible QUBO total-variation formulation for sparse-view CT, but the headline error-free claims rest on per-image hand-tuned weights and highly idealized test images.","tokens_in":11899,"tokens_out":3074,"would_cite":true,"duration_ms":30659,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"QCSTR reconstructs CT images from about 10 percent of the usual projection count.","keywords":["quantum compressed sensing","computed tomography","QUBO","total variation","tomographic reconstruction","X-ray mass attenuation coefficient","hybrid quantum solver","radiation dose reduction"],"falsifier":"Apply the same $Q = aQ_1 + bQ_2$ formulation to a $60\\times60$ phantom whose pixel attenuation values vary continuously over a range rather than taking only values 1, 2, and 3, generate its sinogram from six projections, and solve to the claimed global minimum; if the reconstructed image has more than a handful of wrong pixels, the 'about 10 percent of projections' claim fails for continuous-attenuation objects.","tokens_in":10643,"feed_emoji":"🩻","tokens_out":9991,"duration_ms":95570,"temperature":0.7,"pith_summary":"This paper tries to show that CT image reconstruction can be done from far fewer X-ray projections than classical methods require by posing the problem as a single quadratic unconstrained binary optimization (QUBO) model: a data term that matches simulated projections to measured sinogram data plus a total-variation term that penalizes pixel-to-pixel jumps. The authors test the model with a hybrid quantum-classical optimizer on synthetic anatomical phantoms and on a resized body CT image whose pixels are encoded as three discrete X-ray mass-attenuation values. They report error-free reconstructions of 30x30 images from five projection angles and 60x60 images from six projection angles, about 10 to 20 percent of the projection count normally needed, and recognizable reconstructions from noisy data at 20 percent projections. If this holds, the algorithm points toward cutting CT radiation dose by up to 90 percent while keeping image quality, which matters for medical imaging and for any X-ray tomography setting where dose or scan time is limiting.","feed_headline":"Quantum CT model cuts needed X-ray projections by ~90%","feed_subtitle":"One binary-optimization model with a smoothness term reconstructs error-free images from five or six projections.","key_machinery":"The load-bearing object is the QUBO model $Q = aQ_1 + bQ_2$. QUBO is a quadratic unconstrained binary optimization problem, an energy-minimization problem over binary variables. Here $Q_1$ encodes the squared difference between the simulated projection of the binary-encoded image and the measured sinogram, while $Q_2$ sums squared differences of neighboring pixel values, a total-variation regularizer. The paper encodes pixel values not in binary place-value form but through cumulative X-ray mass-attenuation levels, $I_{ij} = \\alpha_1 q_1^{ij} + \\sum_{k=2}^{m}(\\alpha_k-\\alpha_{k-1})q_k^{ij}$, which makes the $L^1$ and $L^2$ penalties coincide and keeps the solver from getting stuck at the wrong minimum. A hybrid quantum-classical binary quadratic model optimizer minimizes the combined QUBO; the balance between the data term and the smoothness term is set by small integer weights $a$ and $b$, with $(a,b)=(1,1)$ or $(1,2)$ used in the reported error-free cases.","core_discovery":"The paper's central claim is that CT reconstruction can be written as a single quadratic unconstrained binary optimization problem $Q = aQ_1 + bQ_2$, where $Q_1$ is the tomographic data-fidelity term and $Q_2$ is a total-variation smoothness term over adjacent pixels, and that solving this QUBO on a hybrid quantum-classical optimizer returns the global minimum energy associated with the true image. With pixels encoded in the X-ray mass-attenuation-coefficient representation $I_{ij} = \\alpha_1 q_1^{ij} + \\sum_{k=2}^{m}(\\alpha_k-\\alpha_{k-1})q_k^{ij}$, the authors report error-free reconstruction of a $30\\times30$ image from 5 projection angles and a $60\\times60$ image from 6 projection angles, about 10 to 20 percent of the projection count classical reconstruction uses, and recognizable reconstruction from sinograms with about 5 percent Gaussian noise using 20 percent of the projections. The authors interpret the result as a path to cutting CT radiation dose by up to 90 percent once quantum hardware can handle larger QUBO instances.","pith_inferences":["The setup is arguably more a known-material image segmentation or labeling problem than a general CT reconstruction: with pixel values restricted to 1, 2, and 3, the solver is choosing a three-color labeling, and the same QUBO could apply to spectral CT material decomposition where the material classes are known.","The 10-percent projection regime likely depends on the smoothness of the test samples; a stress test with textured or edge-rich phantoms would show whether the ratio degrades, and if so, the projection-count claim should be read as a property of smooth, low-cardinality objects rather than of CT in general.","A natural next experiment is to replace the squared total-variation term with a direct $L^1$-style penalty via auxiliary binary variables; if QUBO size permits, this would test whether the paper's $L^1$/$L^2$ alignment trick is necessary or whether a direct $L^1$ penalty improves robustness on noisy data."],"forward_implications":["A 1000x1000 clinical CT image that normally needs about 1000 projections could in principle be reconstructed from about 100 projections, cutting radiation dose by up to 90 percent.","The same QUBO construction transfers to fan-beam, cone-beam, and parallel-beam geometries and to 3D, because the data-fidelity term only needs the line-integral projection geometry.","With 5 percent Gaussian noise in the sinogram, the algorithm still identifies internal structure from 20 percent of the data, so the dose reduction is not limited to noiseless idealized data.","The optimal weights $a$ and $b$ are not universal: the paper finds different small integer values for different images, so a practical scanner would need an automated rule for choosing them.","If future quantum hardware provides enough qubits for QPU-only solving, the $O(\\log^2 n)$ scaling of the linear-system formulation makes real-time low-dose CT during procedures a plausible target."],"supporting_citations":[{"why":"Provides the QUBO formulation of a linear system that the reconstruction model uses for fast computation.","marker":"[18]"},{"why":"Defines the base quantum tomographic reconstruction QUBO model that the new algorithm extends.","marker":"[19]"},{"why":"Introduces the X-ray mass-attenuation-coefficient pixel encoding that makes the QUBO model reach the desired global minimum.","marker":"[29]"},{"why":"Supplies the total-variation compressed-sensing rationale for adding the smoothness term.","marker":"[34]"},{"why":"Motivates the $L^1$-norm preference and therefore the specific MAC encoding used to align $L^1$ and $L^2$.","marker":"[35]"},{"why":"Supplies the body CT image used in the real-image experiment.","marker":"[36]"},{"why":"Supplies the Gaussian noise model used to test the algorithm on noisy sinograms.","marker":"[37]"}],"fun_headline_variants":["Quantum CT needs just 5 projections for error-free 30x30 image","QUBO-based CT recon from 5 projections: error-free 30x30 images","Quantum compressed sensing CT: 5 projections, zero errors","CT dose cut 90%? Quantum QUBO needs only 5-6 projections","Five projections suffice: quantum QUBO does error-free CT"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The demonstration assumes each pixel belongs to a small set of known materials with known X-ray attenuation values, and that the image has been smoothed so adjacent pixels change continuously; if real anatomy has many materials, unknown coefficients, or sharp edges, far more projections may be needed.","fun_headline_variants_meta":{"raw":{"variants":["Quantum CT needs just 5 projections for error-free 30x30 image","QUBO-based CT recon from 5 projections: error-free 30x30 images","Quantum compressed sensing CT: 5 projections, zero errors","CT dose cut 90%? Quantum QUBO needs only 5-6 projections","Five projections suffice: quantum QUBO does error-free CT"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000714,"raw_usage":{"total_tokens":3257,"prompt_tokens":1035,"completion_tokens":2222,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":651,"completion_tokens_details":{"reasoning_tokens":2122}},"tokens_in":651,"tokens_out":2222,"duration_ms":16257,"temperature":1.0,"reasoning_tokens":2122,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:55:49.246609+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply the same $Q = aQ_1 + bQ_2$ formulation to a $60\\times60$ phantom whose pixel attenuation values vary continuously over a range rather than taking only values 1, 2, and 3, generate its sinogram from six projections, and solve to the claimed global minimum; if the reconstructed image has more than a handful of wrong pixels, the 'about 10 percent of projections' claim fails for continuous-attenuation objects.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the QUBO formulation of a linear system that the reconstruction model uses for fast computation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the base quantum tomographic reconstruction QUBO model that the new algorithm extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the X-ray mass-attenuation-coefficient pixel encoding that makes the QUBO model reach the desired global minimum."},{"cited_title":"Quantum Supremacy in Tomographic Imaging: Advances in Quantum Tomography Algorithms","cited_arxiv_id":"2502.04830","evidence_quote":"Supplies the total-variation compressed-sensing rationale for adding the smoothness term."},{"cited_title":"A quantum approximate optimization algorithm","cited_arxiv_id":null,"evidence_quote":"Motivates the $L^1$-norm preference and therefore the specific MAC encoding used to align $L^1$ and $L^2$."},{"cited_title":"G., & Sidky, E","cited_arxiv_id":null,"evidence_quote":"Supplies the body CT image used in the real-image experiment."},{"cited_title":"V., & Rangan, S","cited_arxiv_id":null,"evidence_quote":"Supplies the Gaussian noise model used to test the algorithm on noisy sinograms."}],"review_version":1}