The 60-qubit result: hardware 17, linear 16, RBF 14

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.

On 21 July 2026, the previously proposed 60-qubit pilot was executed through Fire Opal on ibm_fez. This time, adding width did not merely mean using a larger hash. We replaced the old input with sixty label-free coexpression modules and deliberately kept the circuit shallow.

The fixed held-out test produced the strongest hardware point result in this series:

Route	Balanced accuracy	Correct
60-qubit hardware	0.53125	17/32
classical linear baseline	0.50000	16/32
classical RBF baseline	0.43750	14/32

The hardware execution succeeded, but the small predictive lead and the unfinished MPS comparison do not demonstrate quantum advantage for this QML task.

Relationship to the QOS paper

The 60q pilot is not a literal QOS implementation. The sixty module values are computed classically and loaded as rotation angles in a shallow RY/RZ/RZZ feature map. The route does not contain the paper's random-sample-built query oracle, QSVT/linear solver, or exact classical-shadow readout.

A literal QOS building block exists elsewhere in this project: the separate 4q flat-QOS toy model for \(D=16\) and \(M=64\) implements the official q_state_sketch_flat sampling kernel. Fire Opal action 2334156 reached mean Hellinger fidelity 0.990104 across 64 random kernels. That 4q result validates the sketch kernel, but not the complete classifier. The 60q result validates the wide real-data hardware adaptation, but not the formal oracle chain. Together they form a clear but still incomplete bridge to the paper.

Why the first 60-qubit route failed

Our earlier 60-qubit route obtained 15/32 on hardware, compared with 17/32 ideally and 19/32 classically. The extra qubits mainly carried more hashed input channels. That added width, but not necessarily more stable biological structure.

The new pilot therefore changed the representation, not just the number of qubits:

sixty coexpression modules learned from a fixed, label-free pool of 512 cells;
1,200 variable genes with detection frequencies between 1% and 95%;
deterministic KMeans with random_state=6110 and n_init=20;
four summaries per module: mean log1p, detection fraction, RMS and top-quartile mean;
median/IQR scaling learned from training cells only;
tanh(z/3) and per-block L2 normalisation.

The module pool, training set and test set are mutually disjoint. Test labels played no role in module construction, scaling, model selection or hyperparameter selection.

The 60-qubit circuit

The sixty qubits form a logical 6×10 topology. The feature map uses four input blocks, a sqrt(60) multiplier, logical depth 20 and 134 two-qubit interactions. X, Y and Z measurements yield 627 ordered observables per cell.

Three measurement circuits were built for each of 32 training and 32 test cells:

192 circuits;
128 shots per circuit;
24,576 shots in total;
backend ibm_fez;
Fire Opal action 2335848.

The Fire Opal dashboard reported 26 quantum seconds for this task. That is strikingly short for 192 circuits on sixty qubits. The archived get_result response did not contain this field, so we explicitly identify 26 seconds as the dashboard measurement.

Training-only selection and blind test

Within the training set, cross-validation selected an RBF SVC for the quantum route with C=10 and gamma=0.1. Mean training-only CV was 0.59375; the worst fold remained at 0.50000. The frozen route was then evaluated once on the 32 protected test cells.

On that test, hardware scored 17/32, the linear baseline 16/32 and the RBF baseline 14/32. The one-cell lead over the strongest baseline is small, but for the first time the direction is positive on real hardware.

Why the turnaround time is also interesting

According to the Fire Opal dashboard, the quantum task itself took only 26 seconds. Submission to fully retrieved results took approximately 8 minutes and 33 seconds, including orchestration, compilation, queueing and retrieval. The local MPS check of exactly the same 60-qubit representation ran for 42 minutes and 57 seconds without converging: bond dimension 64 had completed, while at 128 only one of eight required parts had finished.

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.

Statistical boundary

With 32 test cells, one prediction equals 3.125 percentage points. The exact two-sided McNemar p-value against the stronger linear baseline is 1.0. The 95% bootstrap interval for hardware minus linear ranges from -0.1875 to +0.25. A classical lead, a tie and a hardware lead all remain compatible with this small sample.

The next decision gate

The next scientific step is not to spend more quantum time automatically. First, the design must be frozen and the complete classical frontier established for a larger 256/256 split. A large hardware phase would require 1,536 circuits at 128 shots and will receive separate approval only if its information value justifies the Fire Opal budget.