Pillar C · State as of 2026-10-04

Why did the quantum walk lose to classical math on proteins?

As of October 4, 2026, the quantum-walk arm of Rosetta Quantum’s own allosteric-pocket detector has lost its pre-registered match against classical graph mathematics — and the anatomy of the loss is the finding. Under a sealed budget-parity table that gave the quantum side 12 free parameters and the deterministic classical propagators 0, the model using all six propagators failed to out-rank the model using only the three classical ones: paired Wilcoxon p = 0.0949 on 90 proteins, mean delta +0.073, quantum-advantage crossings measured: 0. The loss cannot be blamed on a starved quantum arm — it had the extra knobs and still did not win. The re-match condition is already written: a new pre-registration sealed before the run, the same parity, paired p < 0.05 with positive delta; it will be published whichever way it lands.

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State as of: 2026-10-04

Status as of: October 4, 2026.

What exactly was tested?

Two models identical in everything except three columns. The task is the one our whole engine works on: given a protein’s residue-interaction graph, rank its residues so that the known allosteric pocket lands high — what a quantum walk is, and the full scoreboard of this arm, are already published in our quantum-walk post, and this post does not re-litigate either. The contenders are six “propagators”: per-residue scores produced by spreading something out of the annotated active site across the same contact graph, read in the time window t ∈ [0.5, 8]. Three are quantum, three are classical, and the match was two logistic regressions — identical in regularization, class weighting and folds — one fed all six columns (C_all), one fed only the three classical columns (C_classical). The per-protein metric is the distal percentile of the known pocket; the referee is a contiguous spatial null with 2,000 permutations and a fixed seed. The whole design was sealed before the run in pre-registration PR-QMARGIN-001 (content hash 88d0fbf8, committed_before_run = true) — the anatomy of that pre-registration, and of what a pre-registered negative does and does not license, is in our calibration-of-negatives post.

Propagator	Arm	What it computes	Free params	Source
ctqw_bare	quantum	continuous-time quantum walk exp(−iAt) on the residue contact graph, uniform Hamiltonian	0	Farhi & Gutmann, Phys. Rev. A 58, 915 (1998)
ctqw_glifo_fixed	quantum	CTQW on an annotation-weighted Hamiltonian, weights fixed	0	seal RQ-EXP-QMARGIN-001 (2026-08-03)
ctqw_glifo_learned	quantum	CTQW on an annotation-weighted Hamiltonian, 12 weights learned fold-by-fold	12	seal PARITY-N90 (2026-08-03)
diffusion	classical	heat kernel exp(−Lt) on the same graph	0	Kondor & Lafferty, ICML 2002
gnm	classical	Gaussian network model fluctuation profile	0	Bahar, Atilgan & Erman, Folding & Design 2:173 (1997)
betweenness	classical	shortest-path betweenness centrality	0	Freeman, Sociometry 40:35 (1977)

The 12 learned weights of ctqw_glifo_learned are the quantum arm’s entire wardrobe: a potential over 12 annotation and graph features (UniProt binding/active/domain/PTM/motif sites, ClinVar density, coordination, degree, closeness to the active site, conservation, and GNM/ANM fluctuations), re-learned inside every leave-one-protein-out fold so the arm never sees the protein it is scored on.

What does “same budget” mean — and which side did it favor?

It means every knob was counted and the count was sealed — and if the table favored anyone, it favored the quantum side. Budget parity, the house rule Rosetta applies to every quantum-vs-classical comparison in its ledger, equalizes what actually buys performance: tuning configurations, fits per fold, free parameters, data access, and held-out-only selection, with wall-clock reported but never arbitrating. The instantiated table for this run is sealed as manifest PARITY-N90 (content hash 0a134c23): no arm received per-arm hyperparameter tuning (every regression ran at C = 1.0), and the free-parameter column reads 12 for the quantum walk’s learned potential against 0 for the deterministic classical propagators — diffusion, GNM and betweenness have nothing to tune.

That asymmetry is the anatomical point. When a quantum method loses a benchmark, the first suspicion — ours included — is that the classical side was better fed; we wrote that rule down because it is the first thing we check in other people’s claims. Here the suspicion runs backwards: the quantum arm carried 12 free parameters and three extra columns (7 regression coefficients against 4, counting intercepts), the classical arm carried zero, and the crossings still came out zero. The loss cannot be attributed to a starved quantum arm. What a “crossing” is — the point where a quantum method actually beats your classical baseline — is defined in our crossover-point post.

What came out, number by number?

A precise negative with a positive trend — and every number below is in the sealed result RQ-EXP-QMARGIN-001 (content hash f07244ac). Both variants beat the spatial null decisively (the Fisher combined p rounds to 0.000000 at the six decimals the sealed file records): the propagator family carries real signal about where allosteric pockets live. The pre-registered question was narrower — do the three quantum columns add signal the classical columns do not already carry? The paired one-tailed Wilcoxon returned p = 0.0949, above the declared α = 0.05; the mean pocket-percentile delta was +0.073, with 54 of 89 proteins improved and 35 worsened; and the classical-only variant had more individually significant proteins than the quantum-augmented one, 13 against 11. Re-measured later on the stricter 86-protein no-annotation set, the paired test stayed non-significant — p = 0.0741 and 0.0921, with 1 of 86 proteins individually significant — a marker we already published in the quantum-walk post and do not re-publish here as news.

The reading that fits all of those numbers at once: the quantum columns carry signal, but mostly the same signal the classical columns already carry. The walk did not fail to see the pockets — it failed to see anything the heat kernel, the elastic network and the betweenness count had not already seen. Redundancy, not blindness.

An independent bench reached a strikingly similar shape of answer this year. Mohtashim, Sajjan and Kais measured a CTQW centrality against classical eigenvector centrality on roughly 150 protein residue networks and report a median Spearman correlation around 0.96 between the two rankings, with a modest edge on protein kinase A functional residues (16.75% against 15.21% key score); their own discussion poses the question of “whether CTQW centrality potentially offers any practical advantages over traditional eigenvector centrality calculations” (arXiv:2604.17486, 2026, accessed October 4, 2026). Two independent benches, different tasks, same anatomy: the quantum walk’s ranking lands nearly on top of a classical one.

What did one walk cost on real quantum hardware?

One 12-node circuit, 38.6% of its shots lost to noise — that is the toll recorded in seal RQ-POC-QPU-001 (content hash d026eddc). On August 1, 2026, a continuous-time quantum walk over a 12-residue subgraph of KRAS G12C ran on IBM’s ibm_kingston processor: 2,000 shots, of which 1,228 came back as physically valid one-hot strings (61.4%) and the rest as hardware noise; the device observed 301 distinct bitstrings where ideal dynamics can reach only 12. Of the probability mass that survived, 62.6% landed in the allosteric pocket — structure, not white noise. The logistics are part of the anatomy too: 6 hours 45 minutes in queue for 4.5 seconds of computation, 3 billed seconds. And the seal records its own limits: one circuit reached hardware, not the planned three-depth battery, and the IBM job log does not record the protein or the Trotter depth, which had to be reconstructed from context — our submission protocol changed because of it.

This PoC measures noise resistance, not advantage — the seal itself says so, and marks crossings claimed: 0. Why noisy shots are expensive to recover, and what error mitigation costs, is in our error-mitigation post; nothing in this run changes the N=90 verdict, which was computed in simulation, where the walk pays no noise toll at all. The walk lost its match under the most charitable physics available to it.

What gets re-fought, and what would a win take?

The arm is idle, not retired. Since the detector was frozen for prospective validation, the quantum arm runs again only when a model promotion happens — in the weekly prospective runs it has not run, and QPU spend sits at zero, per our weekly engine state of 2026-09-28 and run-report W40. The victory condition will be the one already exercised once: a new pre-registration sealed before the run, the same parity table, and a paired Wilcoxon p < 0.05 with positive delta. Rosetta will publish it whichever way it lands — the clause that made this loss publishable is the same one that will make a win credible.

What this loss does not license is just as pre-registered. It does not license “quantum walks add nothing”: the trend was positive, and our calibration-of-negatives post walks through why this negative licenses exactly one sentence — no non-redundant quantum signal demonstrated at α = 0.05 on these 90 proteins — and no more. And the loss carries an unresolved attribution we flagged the day we published the marker: we cannot distinguish whether the arm loses because of the physics or because of our graph construction and our features. That sentence is still true, and it is the honest ceiling on every conclusion in this post.

What we don’t know

We do not know whether the walk loses on physics or on our instantiation — a different graph construction, Hamiltonian family or time window could change the outcome, and any such variant will have to be pre-registered and sealed before it runs, like this one was. We do not know whether the positive trend (delta +0.073, p = 0.0949) is a small real effect or noise; the pre-registered test cannot tell, and we will not decide by re-running until something clears the declared threshold. We do not know whether the near-redundancy two benches now report — ours against three classical propagators, Mohtashim, Sajjan and Kais’s 0.96 correlation against eigenvector centrality (arXiv:2604.17486) — comes from the same mechanism, because the tasks and graphs differ. And we do not know how much of the 38.6% hardware noise toll error mitigation would recover, or at what shot cost — we have not measured it.