Four datasets built so a quantum model can demonstrate a potential win
Real industrial data from steel plants, gas turbines, machining lines, and telecom, re-expressed as periodic phases and released on Kaggle today.
There is a pattern in quantum machine learning that everyone in the field has run into and almost nobody says out loud in these terms.
You take a public tabular dataset. You build a variational quantum model. You tune it, you try three encodings, and you try more qubits. Then someone runs a gradient-boosted tree with default parameters and beats you by a margin that no amount of ansatz engineering closes.
The standard response has been to try more datasets. Two weeks ago we published a paper that takes the opposite route: The Fourier Wall (arXiv:2607.15815). The claim is that those contests were unwinnable before the first qubit was allocated and that this is a property of the datasets rather than of the models.
The short version of the argument
An angle-encoded variational quantum model is a partial Fourier series in its inputs. Its accessible frequency set is fixed by the data-encoding gates, not by the variational ansatz. That is a structural fact, not an opinion, and it has consequences you can check.
Every classical model class also has a spectral reach. Additive models capture per-feature structure. Pairwise-interaction models capture order-2 structure. Gradient-boosted trees capture low-frequency structure of any interaction order, given enough splits. Random-feature models capture broad smooth spectra.
A quantum model can only earn a genuine edge where all of those reaches end at the same time. That intersection requires five conditions to hold simultaneously:
The target’s spectrum sits off the integer grid.
The dominant interaction is genuinely joint, of order 3 or higher.
The encoded features are near-independent, because correlation leaks the joint term into low-order projections that classical twins pick up.
The joint coordinate oscillates fast enough that axis-aligned partitioning would need more splits than the data supports.
The joint spectrum is dense beyond enumeration.
That last one is the condition most advantage claims never test, and it is the one that kills the most. If the structure reduces to a few discoverable joint terms, a supervised search writes them down in seconds and a logistic regression with a dozen parameters fits them. In the paper, on a controlled substrate, a classical bar without an order-matched twin credits the quantum model with an advantage at 0.758. Add the twin, which costs about a second of fitting, and the same structure is read classically at 0.968. The advantage dissolves.
Public tabular exports essentially never satisfy the five conditions at once. That is the wall.
The certificate has to be able to say no
The five conditions are testable, so we turned them into SPECTRA, a two-tier go/no-go. Tier 1 screens any tabular dataset in minutes on an ordinary laptop, with no quantum simulator. Tier 2 trains the quantum model against a complete bar of tuned classical twins on identical splits, with paired-bootstrap confidence bounds.
The result we care most about in that paper is a refusal. On real industrial smart-meter data, the real peak-load target, gradient-boosted trees reach a held-out ROC-AUC of 0.999 and SPECTRA returns refuse. A detector that cannot refuse is marketing.
And then the door. On the same real energy phases, carrying the label of an interacting quantum process, the dynamics-matched quantum model reaches 0.994 against a complete classical bar that tops out at 0.699. Clamp the interaction couplings to zero and it collapses to chance, a gap of +0.484. The mechanism is exactly the one the theory predicts.
There is an honest caveat attached to that number, and we keep it attached everywhere we quote it. At seven sites, the exact classical simulator of the same process family ties the accuracy at 0.993, as it must. What separates the lanes is cost: the measured classical per-sample cost grows as 2^1.14n, and the wall-clock crossover against a quantum processor lands at roughly 13 to 19 sites. The certified benefit is a resource separation, not an accuracy miracle.
The gap this release fills
Once you accept the argument, the next question is immediate and annoying: where do you get data on the other side of the wall?
Every public benchmark is, by the paper’s own diagnosis, on the classical side. You cannot test a claim about where quantum advantage lives on data that structurally cannot host it. The negative benchmark literature is evidence about datasets, and repeating it produces no new information.
So today we are releasing four datasets on Kaggle, one per industry substrate, built so the question is at least answerable.
SPECTRA Energy, 35,040 quarter-hour smart-meter records from a steel plant, from UCI 851.
SPECTRA Oil & Gas, 36,733 hourly ambient and process sensor aggregates from a gas turbine, from UCI 551.
SPECTRA Maintenance, 10,000 machining cycles from the AI4I 2020 predictive maintenance dataset, UCI 601.
SPECTRA Telecom, 3,150 telecom customers from the Iranian Churn dataset, UCI 563.
All four substrates are real, popular, CC BY 4.0 public tables with DOIs. The releases are CC BY 4.0 derivatives, and both the original and the release should be cited.
What is real and what is not
This is the part we want to be unambiguous about, because a benchmark that blurs it is worthless.
The covariates are real throughout. Nothing is synthesised on the feature side. The leading genuine fields are additionally re-expressed as continuous periodic phases in the interval from minus pi to pi, which is the representation where cyclic structure survives. This is not cosmetic. In the paper, feeding the same models with variance-maximizing PCA components instead of periodic phases collapses every lane to near chance, while phase features reach 0.752 for the quantum lane and 0.724 for trees. A gap of +0.217 on representation alone. PCA is where periodic structure goes to die.
Part of the label is synthetic, and it is labeled as such. Inside one behaviorally defined segment, the released label additionally reflects an operationally plausible automated campaign: the kind of patterned process that automated usage fraud would produce in a heavy-usage telecom segment or that a demand-response manipulation would produce in heavy-load plant operation. Its structure is chosen so that model families of different expressive order read it differently.
Honesty is built into the schema, not promised in the description. Each release ships three things:
target_real, the original operational label, untouched.target, the benchmark label. Outside the flagged segment it is an exact row-by-row copy oftarget_real. Inside, it keeps every real positive and adds the ones the campaign creates.in_pocket, flagging the affected segment, so challenge hosts can drop the column and everyone else can see exactly where the synthetic component lives.
That gives you three honest evaluations: the real task, the benchmark task, and the difference between them inside the segment, which is precisely where the hidden structure sits.
Results on target must never be quoted as findings about real churn behavior, real turbine emissions, or real machine reliability. Results on target_real are real.
The construction details, the generating parameters and the answer key are retained privately, because a benchmark whose solution ships with it is not a benchmark. The full specification can be shared with reviewers on request.
What we would like people to do with them
Run your lane. Any lane.
If you work on quantum circuits, the interesting question is not whether you beat a default baseline. It is whether you beat a complete bar: trained-frequency GAM, trained-frequency GA2M, gradient-boosted trees, logistic regression, and the order-matched joint twin that most advantage claims omit. Report all of them, on identical splits, with paired confidence bounds on held-out rows.
If you work on classical tabular methods, the same data is a clean question in the other direction: how far does enumeration get, and where does it stop. In the paper, raising the joint twin’s term budget from 6 to 20, or its interaction order to 4, moved it between 0.577 and 0.595 on the dense substrate. The spectrum was dense, not under-enumerated. We would like to see someone try harder than we did.
And if you are running a quantum pilot inside a company, the practical takeaway does not require any of this data. Run tier 1 of the certificate on your own tables first, on a laptop, in minutes, before any hardware spend. A refusal is a result. It is cheaper than a pilot.
SPECTRA itself is in private beta at falcondale.pro. If you want to know which side of the wall your data sits on, the address is contact@falcondale.pro.
Links
Paper: https://arxiv.org/abs/2607.15815
SPECTRA Energy: https://www.kaggle.com/datasets/javierfalcondale/spectra-energy-quantum-ready-steel-plant-data
SPECTRA Oil & Gas: https://www.kaggle.com/datasets/javierfalcondale/spectra-oil-and-gas-quantum-ready-gas-turbine-data
SPECTRA Maintenance: https://www.kaggle.com/datasets/javierfalcondale/spectra-maintenance-quantum-ready-failure-data
SPECTRA Telecom: https://www.kaggle.com/datasets/javierfalcondale/spectra-telecom-quantum-ready-churn-data