Towards secondary structure prediction of longer mRNA sequences using a quantum-centric optimization scheme

Alexey Galda; Chris Cade; Dimitris Alevras; Eline Welling; Ido Niesen; Jae-eun Park; Mariana LaDue; Mihir Metkar; Saurabh Shivpuje; Triet Friedhoff

REVIEW 4 major objections 6 minor 63 references

Towards secondary structure prediction of longer mRNA sequences using a quantum-centric optimization scheme

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict Real hardware at 156 qubits, but the Appendix A reduction is not exact, so the headline results may be for different QUBOs. read the letter →

arxiv 2505.05782 v1 pith:3X22A6UN submitted 2025-05-09 quant-ph

Vaibhaw Kumar , Dimitris Alevras , Mihir Metkar , Eline Welling , Chris Cade , Ido Niesen , Triet Friedhoff , Jae-Eun Park

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Saurabh Shivpuje Mariana LaDue Wade Davis Alexey Galda

This is my paper · ORCID

classification quant-ph

keywords mRNAsecondarystructurepredictionQUBOvariationalquantumalgorithmCVaRoptimizationIQPcircuitsquantum-centriccomputingtensornetworksimulationcombinatorial

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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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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

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.

But 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.

Other 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.

Who 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.

Referee Report

4 major / 6 minor

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.

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 (4)

[Appendix A, Eq. (3) and preceding paragraph] 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 III-A.4 and Section III-C.1, Figs. 4 and 5] 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 III-B.2 and Table I] 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 II, Eq. (2); Section IV] 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.

minor comments (6)

[Fig. 5 caption] 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 III-A.4] 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 III-B.2, Table I] 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 III-A.3, Algorithm 1] 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 III-C] 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.
[References] 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].

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity found; central optima are benchmarked against external CPLEX solutions.

full rationale

The claimed derivations are self-contained rather than circular. The central optimization target is the QUBO of Eq. (2), whose coefficients come from empirical nearest-neighbor thermodynamic parameters (Ref. [48]) and constraint penalties; no quantity in that objective is fitted from the hardware samples or from CPLEX outputs. Both workflows minimize the same Hamiltonian: the CVaR VQA uses hardware samples to update parameters against Hp, and the IQP scheme trains classically on expectation values of Hp and then samples the optimized circuit. The ground-truth optimum used for judging success is computed by CPLEX, an external classical solver, so the reported solutions are not defined in terms of the algorithms' own outputs. Self-citations to Ref. [11] (earlier mRNA QUBO/VQA work) and Refs. [44,45] (IQP expectation optimization) are methodological and are not used as an unverified uniqueness theorem or as the sole justification of the central claim. The Appendix A variable-reduction step is a mathematical reduction of the QUBO; whether its proof is fully sound is a correctness concern, not a circularity, because the reduced problem is not being equated to the original by any self-referential construction. There is no fitted parameter renamed as a prediction and no load-bearing self-citation chain. Hence a score of 0 is appropriate.

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

The ledger shows that the paper introduces no new physical entities, but its central biological claim depends on an unvalidated QUBO energy model, and its practical results depend on several hand-tuned thresholds and an unreported set of QUBO coefficients. The scaling results also depend on the standard MPS representation of shallow circuits and on the classical computability of IQP expectation values.

free parameters (6)

CVaR tail parameter alpha = 0.2
Taken from Ref. [11]; controls the tail of sample energies used as the objective, with no sensitivity analysis in this paper.
Gauge selection threshold p_th = 0.8
Hand-set threshold for deciding which qubits are noisy enough to gauge-flip in Section III-A1; no scan is reported.
Parameter threshold theta_th = 0.06
Set after a few quick hardware runs, as stated in Section III-A2, to improve convergence; this is a tuned hyperparameter.
IQP mitigation threshold <Z_i>_th = 0.99
Predefined threshold for clamping qubits during IQP error mitigation in Section III-C; no sensitivity analysis is shown.
Ansatz depth p = 2
Two entangling layers are chosen for the CVaR ansatz; deeper circuits did not improve tested performance, but depth remains a hand choice.
QUBO reward and penalty coefficients r, p, t = not stated in text
These coefficients in Eq. (2) control stacking reward, UA-end penalty, and crossing penalty; their values are never reported, so the exact objective is not reproducible.

assumptions (6)

domain assumption The quartet QUBO in Eq. (2) accurately represents mRNA secondary structure prediction within the nearest-neighbor model.
The paper adopts the formulation from Refs. [46] and [48] without validating predicted structures against experimental data; if the energy model is wrong, optimal QUBO solutions are not biological predictions.
domain assumption Each base can pair at most once and crossing quartets are forbidden through the penalties in Eq. (2).
These constraints are standard for non-pseudoknotted RNA, but pseudoknots are biologically important and the paper itself notes that pseudoknot prediction is NP-complete.
ad hoc to paper The optimal QUBO bitstring has low Hamming weight, so gauge transformations can map noisy high-weight samples toward the optimum.
Section III-A1 relies on this empirical property of dense problem graphs; it could fail for other sequences or energy parameters.
ad hoc to paper Hardware noise predominantly flips 0 to 1, so single-qubit expectation values below p_th identify noisy qubits.
The gauge and IQP mitigation procedures assume this noise bias; if readout errors are more symmetric, the corrections could distort the objective.
standard math The tensor-network MPS with bond dimension 2^p exactly represents the p-layer circuit used here.
This is a standard property of MPS/MPO contraction for shallow nearest-neighbor circuits, used in Section III-B1.
standard math IQP expectation values can be computed classically in polynomial time for the Hamiltonians used.
The classically-trained IQP scheme relies on Ref. [61] for efficient expectation estimation; this is about expectation values, not about samples, and is used in Section III-C.

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Pith. "Pith review of Towards secondary structure prediction of longer mRNA sequences using a quantum-centric optimization scheme." pith.science (2026). https://pith.science/paper/3X22A6UN

@misc{pith2026250505782,
  author       = {Pith},
  title        = {Pith review of: Towards secondary structure prediction of longer mRNA sequences using a quantum-centric optimization scheme},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3X22A6UN}},
  note         = {Machine review of arXiv:2505.05782}
}

read the original abstract

Accurate prediction of mRNA secondary structure is critical for understanding gene expression, translation efficiency, and advancing mRNA-based therapeutics. However, the combinatorial complexity of possible foldings, especially in long sequences, poses significant computational challenges for classical algorithms. In this work, we propose a scalable, quantum-centric optimization framework that integrates quantum sampling with classical post-processing to tackle this problem. Building on a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the mRNA folding task, we develop two complementary workflows: a Conditional Value at Risk (CVaR)-based variational quantum algorithm enhanced with gauge transformations and local search, and an Instantaneous Quantum Polynomial (IQP) circuit-based scheme where training is done classically and sampling is delegated to quantum hardware. We demonstrate the effectiveness of these approaches using IBM quantum processors, solving problem instances with up to 156 qubits and circuits containing up to 950 nonlocal gates, corresponding to mRNA sequences of up to 60 nucleotides. Additionally, we validate scalability of the CVaR algorithm on a tensor network simulator, reaching up to 354 qubits in noiseless settings. These results demonstrate the growing practical capabilities of hybrid quantum-classical methods for tackling large-scale biological optimization problems.

Figures

Figures reproduced from arXiv: 2505.05782 by the authors.

**Figure 1.** a) Schematic for the quantum-centric architecture for sampling-based quantum optimization using CVaR. The training [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** a) The two-local ansatz with p repetitions of characterized by parameterized Pauli-Y single-qubit rotations and twoqubit CZ gates b) IQP-circuit’s heavy-hex-based tubular arrangement of two qubit e −iθZZ rotation gates on the ibm_kyiv heavy-hex layout with edges between yellow-colored qubits along with all the edges on the heavy-hex graph, shown in green c) parameterized IQP-circuit where D(θ) represents the diagon… view at source ↗

**Figure 3.** Depiction of a single layer of the parameterized [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The converged unnormalized raw objective value distributions from the hardware experiments on [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: a) Convergence plots for the expectation value [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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