{"id":"87fbea86-a256-4efc-986e-af5f07f3a057","arxiv_id":"2505.05782","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Hybrid CVaR and IQP quantum workflows find CPLEX-verified optimal solutions for mRNA-folding QUBO instances up to 156 qubits, but simulated scaling shows steeply declining success rates.","lead":"This paper tests two hybrid quantum-computer and classical-software workflows on the RNA folding problem, using IBM hardware with up to 156 quantum bits and noiseless simulations with up to 354 quantum bits. A generalist should read it to gauge how close quantum computers are to being useful for a real biomedical optimization task, and to see how sharply success rates fall as the problem size grows.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Appendix A's variable reduction is not exact, so the reduced 133/150/156-qubit hardware instances may not solve the original 60-nt mRNA QUBO problems the paper claims.","rationale":"The reader's conditional verdict rests on the biological relevance of the QUBO model, which is a valid concern but is outside the optimization claim itself. My stress-test identifies a more immediate internal correctness issue: the reduction scheme in Appendix A is the mechanism by which 256-variable mRNA problems become the 133/150/156-qubit instances actually run on hardware, and the stated justification for discarding κ variables is mathematically false. The proof relies on the claim that nonnegative quadratic coefficients make all contributions of κ variables nonnegative, ignoring negative linear terms that are present in Eq. (2). The counterexample shows the reduction can change the optimal value even when |h_i| << |J_ij|. Therefore CPLEX verification of the reduced QUBO does not establish optimality for the original mRNA QUBO, and the abstract's claim of solving instances 'corresponding to mRNA sequences of up to 60 nucleotides' is unsupported. This is not a matter of missing baselines or overclaiming scalability; it is a potential flaw in the problem transformation used for all reported large hardware results. The suggested test would settle the issue exactly on a small instance. If the reduction survives the test, the reader's original conditional concerns remain; if it does not, the central demonstration needs to be redone on unreduced instances or with a provably exact reduction.","tokens_in":19389,"tokens_out":9949,"duration_ms":109968,"concrete_test":"Take the smallest mRNA-derived instance used in the paper, construct the full QUBO from Eq. (2) without applying Appendix A, and solve it with CPLEX or an exact ILP solver. Then apply the Appendix A reduction to the same full QUBO and solve the reduced problem. If the optimal values differ, the reduction is not exact and all hardware and tensor-network results on reduced instances must be re-evaluated. As a direct check, run the reduction procedure on the two-variable QUBO Q = -10 z -15 y + 100 z y: the reduction as written returns z=1, y=0 with Q=-10, while the true optimum is z=0, y=1 with Q=-15. If the authors' reduction code instead returns -15, the scheme has an implicit extra condition that must be stated and proven.","verdict_should_be":"REJECT","load_bearing_attack":"The load-bearing step that turns 256-variable problems into the 133/150/156-qubit hardware instances is the reduction scheme in Appendix A, but its correctness proof is unsound. The paper claims that for variables in subset κ, whose quadratic coefficients are all nonnegative, 'their contributions to Q will always be ≥ 0', so those variables can be discarded and optimized later. This is false when a κ variable has a negative linear coefficient h_i and no selected neighbor: the linear term then lowers Q, so discarding it can change the optimum. Eq. (2) includes negative nearest-neighbor free energies, so such negative linear terms are expected. A minimal counterexample is h_z = -10, h_y = -15, J_zy = 100, with y ∈ κ. The reduced problem over z alone yields z = 1, Q = -10; fixing z = 1 makes y = 1 costly (+85), so the reduction reports -10. The true optimum is z = 0, y = 1, Q = -15. The paper's later sentence acknowledging that variables with h_i < 0 can lower Qκ is inconsistent with the earlier claim that all contributions of κ variables are nonnegative. Because the reduction is applied before CPLEX verification and before the hardware runs, the demonstrated optima are for a different QUBO unless the reduction is proven exact. The nested optimization also fixes non-κ variables to the Q_red optimum before optimizing κ, so it cannot detect trade-offs where a slightly worse reduced solution enables a much better κ assignment.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes two quantum-centric workflows for solving QUBO formulations of mRNA secondary structure prediction: a CVaR-based variational algorithm enhanced with gauge transformations, parameter thresholding, and classical local search, and a classically trained IQP circuit whose optimized parameters are sampled on quantum hardware with subsequent error mitigation and local search. The authors report hardware experiments on IBM processors with 127-156 qubits, tensor-network simulations up to 406 qubits, and CPLEX-verified optimal solutions for several reduced instances. An appendix describes a variable-reduction scheme used to map 256-variable problems down to 133/150/156-qubit instances, and the stated claim is that mRNA sequences of up to 60 nucleotides can be tackled at this scale.","tokens_in":19750,"tokens_out":9596,"duration_ms":97503,"significance":"If the optimization claims hold, this is a useful engineering demonstration of hybrid quantum-classical optimization on utility-scale hardware, with practical details (gauge transformations, parameter thresholding, IQP expectation-based training, and an exact MPS contraction scheme) that could inform future work. The paper provides machine-checkable CPLEX verification of the reduced instances and reproducible algorithmic descriptions. However, the significance is currently limited by an unsound reduction proof, the absence of classical baselines, and an internal inconsistency in the tensor-network scalability results; these issues must be resolved before the central claims about 'solving' 60-nucleotide mRNA problems can be accepted.","major_comments":[{"comment":"The reduction scheme is not exact, and the proof given is internally inconsistent. The paper first claims that variables in κ 'contributions to Q will always be ≥ 0' because their quadratic coefficients are nonnegative, but this ignores negative linear coefficients h_i; two sentences later it concedes that variables with h_i < 0 can lower Qκ. A concrete counterexample satisfying the paper's own condition |h_i|≪|J_ij| is: h_z = -1, h_y = -2, J_zy = 100, with y∈κ and z∉κ. Solving Qred over z yields z=1 with value -1; optimizing κ with z fixed gives y=0 and total -1, but the true optimum of the full QUBO is z=0, y=1 with value -2. Since the 133/150/156-qubit hardware instances are obtained by applying this reduction to 256-variable problems, the CPLEX-verified optima and the claimed '60-nucleotide' results are for the reduced QUBO, not for the original mRNA problem. The authors must prove exactness under the stated assumptions (which the counterexample shows is impossible without additional restrictions), verify the original instances with CPLEX or another exact solver, or explicitly re-scope the claims to the reduced problems.","section":"Appendix A, Eq. (3) and preceding paragraph"},{"comment":"No classical baseline is reported on the same instances. The paper does not state how often the local-search post-processing alone (from random or trivial starting bitstrings, or from classically simulated samples) reaches the CPLEX-verified optimum, nor does it compare the hardware samples with samples drawn classically from the same trained distribution. Without such an ablation, the specific contribution of the quantum processor to the claimed 'solving' of these instances is not established.","section":"Section III-A.4 and Section III-C.1, Figs. 4 and 5"},{"comment":"There is an internal inconsistency in the tensor-network scalability claim. The text states that 'Applying this strategy, we successfully solve the 354-qubit problem instance,' but Table I reports 0 hits out of 100 for 354 qubits both without and with post-processing, with relative errors of 21.4% and 10.5%. If the table refers to a baseline before the resume-from-best-parameter strategy, this must be stated clearly; otherwise the reported simulation results contradict the table.","section":"Section III-B.2 and Table I"},{"comment":"The manuscript does not validate the QUBO model as a predictor of mRNA secondary structure. No comparison is made to experimentally determined structures or to standard classical predictors (e.g., ViennaRNA) on the same sequences, and no discussion of the mapping from a QUBO optimum to an actual secondary structure is provided. The title and abstract claim 'secondary structure prediction,' but the demonstrated results are solutions to a QUBO whose biological fidelity is unexamined. The authors should either add structural validation or explicitly limit the paper's claims to QUBO optimization.","section":"Section II, Eq. (2); Section IV"}],"minor_comments":[{"comment":"The caption says '127 and 150 qubit problems' and 'optimal objective values of -161.5 and -249.1 for the 127 and 150 qubit problems respectively,' but the text and panel (c) describe a 156-qubit problem; the caption should be corrected.","section":"Fig. 5 caption"},{"comment":"The mapping of sequence lengths to qubit counts is confusing: the 133-qubit and 150-qubit problems are said to originate from sequences of length 60 and 48, while the 156-qubit IQP problem is said to come from a 60-nucleotide sequence. Clarify which sequence is used for each experiment and why the reduced sizes differ so much for the same sequence length.","section":"Section III-A.4"},{"comment":"The table reports γ as 'relative error' but the definition in the text (|F(θf)_low - F0| / |F0|) is for the lowest value over all samples at any time; clarify whether the table entries for the 'no post-processing' column use raw samples or the best parameter configuration over the run.","section":"Section III-B.2, Table I"},{"comment":"The sentence 'for j in Permute(x)' should be 'for j in Permute({1,...,n})' to be precise. Also, the bound Δ = 2(Σ_i h_i + Σ_{(i,j)∈G} J_{ij}) for the maximum decrease of the local search is incorrect when h_i or J_{ij} are negative; for a starting all-zero bitstring with negative h_i and positive J_{ij}, the bound can be negative while the attainable decrease is nonnegative.","section":"Section III-A.3, Algorithm 1"},{"comment":"The phrase 'the expectation calculation ... consists of computing averages over bit strings generated randomly from a uniform distribution' should be more explicit that this is a classical Monte Carlo estimate using finitely many samples (2^15), not an exact evaluation; the approximation error is not discussed.","section":"Section III-C"},{"comment":"Reference [28] has an incomplete title ('Does provable absence of barren plateaus imply classical simulability, Or, why we need to rethink variational quantum computing'); also, the paper's claims about 'classically difficult' IQP sampling should acknowledge the noisy-regime caveat more prominently than the single reference to Ref. [43].","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The reduction flaw in Appendix A is the most serious issue; I would want to see either a corrected proof, a demonstration that the reduced and original optima coincide for the specific instances (e.g., exact CPLEX solutions of the original 256-variable problems, if feasible), or a rescaled claim. The paper is otherwise a reasonable engineering demonstration, but the absence of classical baselines and the table/text inconsistency also need to be resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper reports genuinely large experiments: 133/150/156-qubit hardware runs and tensor-network simulations up to 354 qubits, with a clear description of the CVaR, gauge-transformation, and IQP workflows. That is worth a look. The IQP expectation derivation in Appendix B is neat, and the paper is honest about hit rates dropping to zero at the larger tensor-network sizes. \n\nBut there is a load-bearing problem in Appendix A. The reduction scheme claims that variables in set κ contribute only nonnegatively to Q, so they can be optimized separately after solving the reduced problem. That is simply false when a κ variable has a negative linear coefficient, as the paper's own Eq. (2) allows. The text even contradicts itself: first it says κ contributions are always ≥ 0, then later admits that variables with h_i < 0 and zero quadratic coupling can lower Qκ. The counterexample in the stress-test note is correct: a variable with h_z = -10, h_y = -15, J_zy = 100 under the reduction gives optimum z=1 with Q=-10, while the true optimum is z=0, y=1, Q=-15. The reduction is not exact, and since it is applied before both CPLEX checks and hardware runs, the demonstrated optima are for the reduced QUBO, not necessarily the original 256-variable mRNA problem. That undermines the central claim of solving 60-nt problems at 156 qubits. \n\nOther soft spots are secondary but real: no classical baseline on identical instances, no ablation separating quantum samples from the local-search post-processing, no sensitivity analysis for the tuned thresholds, and no validation of the QUBO model against experimentally known mRNA structures. The biological claim is therefore unverified regardless of the optimization result. The tensor-network scalability also needs a caveat: at 354 qubits the algorithm finds the optimum in only a small fraction of runs even with post-processing, so the statement that it \"successfully solves\" those instances overstates the hit rate. \n\nWho is this for? People working on quantum-centric hybrid optimization and IQP-based sampling will find the experimental details useful. Anyone interested in actual mRNA secondary structure prediction should wait until the QUBO is benchmarked and the reduction is either proven or replaced. I would send it to peer review, because the hardware experiments are substantial and the methods deserve scrutiny, but the author response must address the reduction error head-on. Without that fix, the paper's headline is not supported.","headline":"Real hardware at 156 qubits, but the Appendix A reduction is not exact, so the headline results may be for different QUBOs.","tokens_in":20289,"tokens_out":2267,"would_cite":false,"duration_ms":25108,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that hybrid quantum-classical optimization can find certified optimal solutions to the mRNA-folding QUBO at 156 qubits, corresponding to 60-nucleotide sequences.","keywords":["mRNA secondary structure prediction","QUBO","variational quantum algorithm","CVaR optimization","IQP circuits","quantum-centric computing","tensor network simulation","combinatorial optimization"],"falsifier":"Run the same mRNA sequences through the two workflows many times, then compare every final post-processed bitstring against the exact optimum found by a classical exhaustive solver for instances up to 156 qubits; if the post-processed hit rate is far below the paper's reported results, the optimization claim is falsified. Separately, take the optimal QUBO bitstrings for a panel of mRNAs with experimentally known structures and compare the predicted base pairs to the measured ones; if the agreement is no better than chance, the biological motivation is falsified even though the optimization succeeded.","tokens_in":19186,"feed_emoji":"🧬","tokens_out":9907,"duration_ms":103918,"temperature":0.7,"pith_summary":"mRNA secondary structure is the pattern of base pairing a messenger-RNA chain folds into, and predicting it is a combinatorial optimization problem. The paper turns this into a QUBO instance whose variables are stacked base-pair quartets, then attacks it with two quantum-centric workflows: a variational circuit trained with a tail-averaged energy objective (CVaR), a bit-flip gauge transformation, parameter thresholding, and classical local search; and an IQP circuit whose parameters are trained classically while the quantum processor only samples from the optimized circuit, followed by error mitigation and local search. The central claim is that these workflows reach the exact optimum for the tested instances, with optimality verified by an exact classical solver, at problem sizes up to 156 qubits and circuits with up to 950 nonlocal gates, corresponding to mRNA sequences of up to 60 nucleotides. The paper further claims that the CVaR workflow, simulated without noise via tensor networks, remains viable up to 354 qubits, with hit rates declining as size grows but with classical post-processing recovering near-optimal samples. A sympathetic reader would care because this is a biologically motivated instance of a quantum-centric optimization template operating at utility scale, and because the IQP route separates the classically easy training step from the presumably hard sampling step.","feed_headline":"Quantum-classical workflows solve mRNA QUBOs to 60 nucleotides","feed_subtitle":"A quantum sampler plus classical search reaches verified optimal foldings for 60-nucleotide sequences.","key_machinery":"The load-bearing object is the QUBO in Eq. (2), whose binary variables are quartets, two consecutive base pairs written as $(i,j,i+1,j-1)$. Its energy coefficients come from empirical nearest-neighbor thermodynamics; a reward $r$ strengthens consecutive stacked quartets, a penalty $p$ discourages quartets ending in a UA pair, and a penalty $t$ forbids crossing quartets. Two mechanisms carry the variational workflow: the CVaR objective, which averages the lowest $\\alpha=0.2$ tail of sampled energies and makes updates more robust to noise; and the bit-flip gauge transformation, which relabels eigenstates so that the hardware's noisy Hamming-weight bias matches the low-weight solutions expected of these dense problems. For the IQP route, the key identity is Eq. (5): expectation values of the parameterized IQP circuit reduce to a cosine sum over uniformly random bitstrings, so training can be done classically, while sampling from the circuit's output distribution is the part delegated to quantum hardware. The tensor-network simulation exploits the fact that each ansatz layer is a matrix-product operator of bond dimension 2, making exact contraction linear in qubit count for the two-layer circuits used.","core_discovery":"On its own terms, the paper's discovery is that hybrid quantum-classical optimization can solve the specific QUBO instances derived from mRNA folding to proven optimality, not merely to good approximate energies. For the CVaR-based workflow, 133- and 150-qubit instances from 60- and 48-nucleotide mRNAs were run on real quantum processors, and for the IQP-based workflow, 127- and 156-qubit instances from 45- and 60-nucleotide mRNAs; after the classical local-search post-processing, the exact optimal objective values were found. In noiseless tensor-network simulations of the same CVaR algorithm, the method tracked the optimum up to 354 qubits, sometimes only after resuming from the best parameter configuration seen in an epoch, and the relative error of the best samples grew with system size. The paper presents this as evidence that the practical capability of quantum-centric methods for large biological optimization problems is growing, while being explicit that no performance guarantees follow from the heuristic nature of the schemes.","pith_inferences":["Because optimality is certified only against the QUBO objective, a natural next test is to score the same optimal bitstrings against experimentally characterized mRNA structures; if systematic mismatches appear, the energy coefficients or penalty weights in Eq. (2) would need retuning rather than the quantum pipeline.","The bounded improvement of the local search means the real benchmark for these workflows is the distance between the mitigated quantum samples and the optimum; a useful extension would probe whether stronger gauge selection or shallower circuits shrink that distance at 300 or more qubits.","The IQP route's classical trainability raises a spoofing question the paper does not answer: if a classical sampler can mimic the mitigated output distribution, the quantum sampling step would be redundant. Comparing quantum hardware samples with classical samples from the same optimized IQP circuit would settle that empirically.","The variable-reduction scheme the paper uses to shrink 256-variable problems to 133 or 156 qubits is itself a transferable tool; applying it to other high-edge-density QUBOs could make the quantum-centric template useful beyond RNA folding."],"forward_implications":["For mRNA sequences up to 60 nucleotides, the demonstrated recipes give a path to certified optimal QUBO solutions with roughly 156 qubits and up to 950 nonlocal gates, roughly doubling the 80-qubit / 42-nucleotide scale previously reported.","The noiseless tensor-network results support the claim that the CVaR workflow can operate at 354 qubits, so the practical ceiling for longer sequences is set mainly by hardware noise and the expressivity of the shallow ansatz, not by the optimization principle.","The IQP scheme can be run with fully classical training, meaning the expensive variational loop is moved off the quantum processor and the hardware's role is reduced to sampling a fixed optimized circuit.","The gauge-transformation plus parameter-threshold plus local-search post-processing stack is independent of the specific mRNA instance and should transfer directly to other dense QUBO problems whose optima are low-Hamming-weight bitstrings."],"supporting_citations":[{"why":"Establishes the earlier 80-qubit, 42-nucleotide mRNA QUBO experiments that this work scales up and compares against.","marker":"[11]"},{"why":"Introduces CVaR as the variational objective and supplies the tail-averaging used in all parameter updates.","marker":"[32]"},{"why":"Provides the quartet stacked-pair variable formulation and the crossing-pair constraint used in Eq. (2).","marker":"[46]"},{"why":"Supplies the empirical nearest-neighbor free energies and the UA-pair stability penalty used as coefficients.","marker":"[48]"},{"why":"Presents the spin-reversal gauge transformation adapted here to align hardware samples with low-Hamming-weight solutions.","marker":"[50]"},{"why":"Defines the single-parameter-coordinate optimizer used for the classical parameter updates.","marker":"[52]"},{"why":"Provides the library for computing IQP expectation values classically, enabling fully classical training of the IQP circuit.","marker":"[44]"},{"why":"Supplies the complexity argument that sampling from IQP circuits is classically hard, motivating the quantum sampling step.","marker":"[40]"},{"why":"Extends the IQP hardness to average-case approximate simulation, supporting the use of optimized IQP circuits as samplers.","marker":"[41]"},{"why":"Introduces the matrix-product-state methods used to simulate the CVaR workflow to 354 qubits.","marker":"[33]"}],"fun_headline_variants":["Quantum-classical hybrid folds mRNA up to 60 nucleotides","Hybrid quantum scheme optimizes mRNA folding to 60 bases","Quantum-centric QUBO solver reaches 60-nucleotide mRNA","Quantum + classical search solves mRNA QUBOs to optimality","mRNA secondary structure via quantum-centric optimization: 60 nt"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The biological meaning of the whole exercise rests on one unvalidated premise: that the quartet QUBO with empirical nearest-neighbor energies and the chosen penalty weights is a faithful model of real mRNA secondary structure, and the paper never checks its predicted foldings against experimentally determined RNA structures.","fun_headline_variants_meta":{"raw":{"variants":["Quantum-classical hybrid folds mRNA up to 60 nucleotides","Hybrid quantum scheme optimizes mRNA folding to 60 bases","Quantum-centric QUBO solver reaches 60-nucleotide mRNA","Quantum + classical search solves mRNA QUBOs to optimality","mRNA secondary structure via quantum-centric optimization: 60 nt"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000568,"raw_usage":{"total_tokens":2699,"prompt_tokens":962,"completion_tokens":1737,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":578,"completion_tokens_details":{"reasoning_tokens":1652}},"tokens_in":578,"tokens_out":1737,"duration_ms":15175,"temperature":1.0,"reasoning_tokens":1652,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:56:50.761224+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same mRNA sequences through the two workflows many times, then compare every final post-processed bitstring against the exact optimum found by a classical exhaustive solver for instances up to 156 qubits; if the post-processed hit rate is far below the paper's reported results, the optimization claim is falsified. Separately, take the optimal QUBO bitstrings for a panel of mRNAs with experimentally known structures and compare the predicted base pairs to the measured ones; if the agreement is no better than chance, the biological motivation is falsified even though the optimization succeeded.","supporting_citations":[{"cited_title":"Optimizing the spin reversal transform on the d-wave 2000q,","cited_arxiv_id":null,"evidence_quote":"Presents the spin-reversal gauge transformation adapted here to align hardware samples with low-Hamming-weight solutions."},{"cited_title":"Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy,","cited_arxiv_id":null,"evidence_quote":"Supplies the complexity argument that sampling from IQP circuits is classically hard, motivating the quantum sampling step."},{"cited_title":"Average-case complexity versus approximate simulation of commuting quantum com- putations,","cited_arxiv_id":null,"evidence_quote":"Extends the IQP hardness to average-case approximate simulation, supporting the use of optimized IQP circuits as samplers."}],"review_version":1}