What is still required for quantum advantage?

Project status — 20 September 2026

Unfortunately, no quantum advantage has been demonstrated for the QML task studied here. We have not established a time saving at the same useful predictive quality against a strong classical approach. Higher accuracy is not required: equally good predictions in less total time would suffice.

The earlier comparison with an unfinished MPS simulation does not establish that advantage. A classical classifier does not have to simulate the quantum circuit to solve the classification task. The hardware experiments below remain research results, not evidence of practical QML advantage. The project is listed under Work and has been removed from the Advantage List.

What the latest checks show

  • Hardware: Fez with Fire Opal scored 17/32, the Nighthawk replay 16/32, the classical linear reference 16/32 and RBF 14/32. The Nighthawk classifier also predicted the same class for every test cell. This small, reused test set establishes neither predictive advantage nor a practical speedup.
  • Longer streaming study: an exact classical calculation processes 128 training and 4,096 test cells in a median 1.12 seconds, excluding loading and one-time preparation. The frozen model scores 2,059/4,096 (50.27%) on those new test cells. No corresponding quantum runtime was measured for that same task.
  • Latest local circuit study: 16 variants and four input-basis repairs were examined. Broad correlations were either identically zero or very small compared with shot noise. The repaired variants achieved approximately 48–51% validation accuracy in an ideal 512-shot model, versus 54.69% for the frozen classical reference. These are local calculations and simulated measurements, not new QPU results; 23 focused tests passed.
  • Separate discrete-log investigation: the latest follow-up report discusses a specialized classical check and a count of quantum arithmetic resources. It also provides no measured quantum runtime. A resource investigation of that different QML task is not hardware evidence for this PBMC series.

Conclusion: this educational research project produced working hardware experiments, but did not achieve its intended quantum advantage. This does not establish that quantum advantage is impossible for every QML task. The QOS paper's theory, assumptions and logical qubits remain distinct from our physical-hardware experiments.

The 60-qubit pilot of 21 July 2026 provides the first positive hardware point result: 17/32 versus 16/32 for linear and 14/32 for RBF. This is a serious reason to continue testing, but not proven advantage. A credible quantum-ML claim still requires positive answers to three different questions at once: does the model generalise, is the quantum route demonstrably hard to match within the selected classical resource bound, and is the end-to-end resource accounting correct?

1. Demonstrate generalisation first

A follow-up study needs more independent cells. That means not only a larger test set, but also several predeclared splits or donors. A useful minimum programme is:

  • select models and observables using training data only;
  • use several fixed, balanced train/test splits;
  • retain a completely untouched final test cohort;
  • report balanced accuracy, AUC, calibration and per-class errors;
  • report confidence intervals and a preselected paired test;
  • check biological stability across donors or batches.

With 32 test cells, one cell can reverse the conclusion. With hundreds of test cells, a small but consistent difference can be assessed much more reliably.

2. More hardware data, not merely more qubits

Forty or sixty qubits sound impressive, but width alone does not solve sample scarcity. Both 405 features in the 40-qubit route and 627 observables in the new 60-qubit route face only 32 training cells. This remains statistically unfavourable. Possible improvements include:

  • run more training cells on hardware;
  • reduce the observable panel using training data only;
  • execute several independent 128-shot runs;
  • measure calibration drift across days;
  • compare shot budgets;
  • incorporate uncertainty in quantum features into the classifier.

A sixty-qubit circuit can be kept shallower, but it still requires careful readout and batch design. The small sentinel was allowed as a feasibility test when the planned MPS convergence check could not be completed within the available time. A large hardware phase still requires training-only stability, a frozen design and separate approval.

3. Build an explicit bridge to the complete QOS algorithm

The 4q flat-QOS pilot has now validated one genuine building block: samples construct the official phase sketch and interference makes that sketch measurable. That kernel is not yet connected to the PBMC68k classifier. Conversely, the 60q route uses real PBMC68k data, but it does not attempt to approximate a formal QOS oracle: it replaces that component with four blocks of classically computed rotation angles, short layers and local Pauli readout.

A testable next bridge could pad the sixty gene modules to 64 values, translate them training-only into a compact sample distribution, and process that through a 6q flat-QOS sketch. Only then should the work examine general real values, a reusable query oracle, QSVT and the decision function. This bridge must make explicit:

  • which part of the QOS oracle is implemented literally and which part is replaced;
  • how approximation error scales with blocks, shots and depth;
  • which QSVT or linear-solver steps are missing;
  • whether the 405-feature classifier approximates the same decision function as the theorem’s LS-SVM;
  • how much classical side information is required for hashing and circuit control.

Without that bridge, “QOS-inspired” is more accurate than “hardware implementation of Theorem 3.”

4. A stronger classical frontier

The classical opponent must be assessed both practically and under explicit resource constraints. At minimum we need:

  • sparse logistic regression and LinearSVC on all genes;
  • feature selection using training data only;
  • hashing, sparse JL and streaming models with measured memory;
  • PCA/SVD and kernel routes;
  • biological marker baselines;
  • tensor-network or causal-cone analysis of the specific quantum circuit;
  • runtime, RAM, model size and energy as separate columns.

The official QOS repository added sparse JL projections in May 2026. This matters because the classical frontier moves. An advantage claim must be repeated against the latest strong baseline rather than the baseline available when the project started.

5. Which kind of advantage do we mean?

“Quantum advantage” can refer to different claims:

Claim Required evidence
predictive advantage significantly better held-out performance
space advantage the same task performance using demonstrably less working memory
time advantage lower fair end-to-end time at the same error tolerance
sample advantage fewer data points needed for the same generalisation
scaling advantage more favourable measured growth with problem size

QOS theory mainly concerns machine size and, in dynamic cases, sample complexity. Our pilot mainly measures hardware feasibility and predictive accuracy. These remain different axes.

A realistic experimental ladder

After the successful 60-qubit sentinel, the route forward has five new gates:

  1. Freeze the representation: retain the sixty label-free gene modules, 627 observables and classifier selection without test feedback.
  2. Broaden the classical frontier: add sparse linear, kernel, marker, JL and streaming baselines with measured time and memory.
  3. Larger local splits: test 256/256 and several preselected seeds before using more hardware time.
  4. Large hardware confirmation: execute the frozen design on more cells only after separate approval and record every batch cost.
  5. Final blind test: evaluate one untouched cohort and publish a null or negative outcome as well.

Only when the quantum route performs better on the final blind test, or matches performance with convincingly lower measured resources, does an empirical advantage claim emerge.

What can we already say?

The updated conclusion of this series is: unfortunately, no demonstrated quantum advantage for the QML task studied.

We withdraw the earlier description "time-to-feature-generation advantage" as a project conclusion. Historically, 26 quantum seconds and about 513 seconds through retrieval were compared with an MPS attempt that remained unfinished after 2,577 seconds. The ratios greater than 99.1x and 5.0x are not a matched speed measurement: MPS produced no converged answer at the same error, and a strong classical classifier need not simulate this feature map. No quantum advantage has therefore been demonstrated for the complete QML task. The hardware-oriented QOS-inspired 40q/60q feature map is not a literal QOS implementation or the complete QOS/QSVT algorithm.

Part 8 gives the executed 60-qubit protocol, the 17/32 outcome, timing and statistical boundary in full.

Sources and code