Evidence, not promises
Published benchmark runs — numbers unedited.
Every figure on this page is unedited solver output from the published RQP sample reports — the same certified PDFs you can download in the Resource Room. The flattering numbers and the boring ones, including the run where our own product recommended staying classical.
Portfolio Optimization RQP · published sample run
What an honest quantum benchmark looks like
78 assets, aggregated into 23 binary decisions (17 single names + 6 thematic bundles), 3 sector-budget bands, QAOA depth p=4 — every one of the 8.4 million possible portfolios evaluated exactly, against a certified classical referee.
8,388,608
Portfolios evaluated — every single one
Exact 2²³ state readout, no sampling noise
0.0%
QAOA gap to certified optimum
Best QAOA portfolio = SCIP-proven optimum, bit for bit
+3.2%
Classical heuristic gap
465 heuristic candidates — none reached the optimum
137×
Odds boost for the optimal state
vs uniform sampling — yet still 0.0016%, and the report says so
Winning portfolio: 8.0% expected return · 15.3% volatility · Sharpe 0.33 · budget gap 0.08% Run: 2 h 28 min certified end-to-end · warm-started p=4 · statevector simulator · seed 42, reproducible
- ✓
Verified, not asserted. QAOA's best portfolio equals the referee's proven optimum — gap 0.0%, certified by exact branch & bound (MIQP/SCIP) — while the classical heuristic fell 3.2% short.
- ✓
No magic claimed. The optimum's sampling probability was 0.0016% — a 137× boost over uniform, and still a small number. Both figures are printed in the report.
- ✓
Scale is stated, not implied. Simulator memory doubles with every qubit — around 30 is where real hardware has to take over. Prototyping below that line, with a referee, is how you build a quantum case you can defend.
Index Replication RQP · published sample run
Your mandate rules have a price. The quantum benchmark certifies it.
Enhanced-indexing the S&P 500 with 20 instruments: 500 assets in the objective, 17 selection qubits — and a referee that re-solves the mandate to price every rule in tracking error.
4.473%
Certified minimum tracking error
SCIP dual bound proves no basket beats it · MIP gap 0
0.00%
QAOA gap to certified optimum
Its basket is a certified-optimal one
+3.39%
Greedy heuristic gap
The industry-standard shortcut missed; random baseline +1.20%
The constraints landscape — every rule priced by the referee
Certified cost = optimum re-solved with only that rule removed. Unedited from the report.
Technology band
4–6 names required · landed at 6
+0.332%
Climate-transition band
2–4 names required · landed at 4
+0.339%
Both rules together
the package overlaps — it costs no more than its strictest rule
+0.339%
The irreducible floor: the instrument pool and exclusions alone impose 3.098% tracking error before any mandate rule applies.
Run: 110 s end-to-end · QAOA 53.8 s (p=2, 3 restarts, exact readout) · referee proof 11.2 s · 17 qubits, 544 two-qubit gates
- ✓
Constraints stop being opinions. Each mandate rule is priced by re-solving the certified optimum with only that rule removed. The mandate discussion becomes numbers, not beliefs.
- ✓
The irreducible floor is stated. The instrument pool and exclusions alone impose 3.098% tracking error before any rule applies — whatever the pool cannot replicate shows up openly, not hidden in a heuristic.
- ✓
No magic claimed. Only 3.6% of raw quantum readout hit the 20-name cardinality; candidates were repaired, and the best one reached the optimum after a single disclosed polish swap. On today's hardware this 544-two-qubit-gate circuit would retain ~7% fidelity. It's all printed in the report.
QML Classification RQP · published sample run
Don’t bet on quantum. Measure it.
Classifying German power-price spikes with an 8-qubit quantum kernel against six tuned classical baselines — 17,157 rows, an exact 10,294×10,294 quantum kernel, paired bootstrap statistics. For this dataset the measured answer was “not yet” — and that verdict is the product working as designed.
34/100
QML suitability score — this dataset
“Too simple for quantum” — every dataset is scored before a single circuit runs (±12)
0.92×
Advantage factor, raw features
95% CI 0.896–0.937, entirely below 1.0 — classical clearly ahead
0.99×
Advantage factor, Fourier-engineered features
95% CI 0.975–1.011, includes 1.0 — “inconclusive within noise”
1 day
The cost of knowing
Verdict for this dataset, today: keep the classical model — re-tested as encodings and hardware evolve
- ✓
The bar is real. Quantum is scored against tuned classical baselines — including a periodic Fourier probe that absorbs exactly the structure an angle-encoded quantum model could pass off as “advantage” (methodology after the Fourier Wall paper, arXiv:2607.15815).
- ✓
Statistics, not vibes. An advantage is claimed only when the whole 95% confidence interval sits above 1.0. Better feature encoding moved the factor from 0.92 to 0.99 — a measured trajectory, not a promise.
- ✓
A verdict about one dataset — not about quantum. Other data profiles score differently; that is what the suitability filter is for. And “let's revisit later” only works if someone is measuring: the harness re-runs as encodings and hardware evolve, so the week the interval clears 1.0, you know.
Sources & scope
Portfolio run: published sample report of 16 Jul 2026 (78-asset demo universe). Index run: published sample report of 12 Jul 2026 (S&P 500 demo mandate, 20 ISINs). QML runs: published sample reports of 23 Jul 2026 (German power-price spike demo dataset, baseline & Fourier-engineered). All reports are gated downloads in the RQP Resource Room. All figures are unedited solver output on demo data — illustrative only, not investment advice, not indicative of results on other problems.
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