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.
Quantum machine learning is often described as if a quantum computer searches an entire database at once. Our experiment does something more precise and more interesting: it attempts to predict the cell type of a single cell from its gene-expression profile. The input is a long, sparse vector of RNA counts; the output is one of two immune-cell classes.
This learning path starts with a four-qubit tutorial and continues with an eight-part series connecting four layers that are easily confused. The first is the theory of Quantum Oracle Sketching (QOS), published in April 2026. That theory concerns a small quantum model processing massive classical data streams without retaining the entire matrix. The second layer is the official JAX code and its numerical PBMC68k experiments. The third is our literal flat-QOS sketch on four qubits: a bounded port of the official sampling kernel, physically executed on IBM Fez. The fourth consists of our 40- and 60-qubit PBMC68k routes. Those are QOS-inspired NISQ feature maps, explicitly not literal implementations of the complete QOS/QSVT algorithm.
The new 60-qubit run is the strongest result in the series. On the predeclared held-out test, hardware scored 17/32, compared with 16/32 for the linear and 14/32 for the RBF baseline. The Fire Opal dashboard reported only 26 quantum seconds, and the complete hardware feature output was retrieved after about 8 minutes 33 seconds. Our classical MPS attempt had not produced a converged reference after 42 minutes 57 seconds.
The series
- Tutorial: from UMI counts to a four-qubit circuit
- What is the QML task? Classifying cells, not looking up genes
- The theory of Quantum Oracle Sketching
- From PBMC68k gene expression to 40 qubits
- From JAX to a 40-qubit hardware circuit
- 405 observables and a leakage-free classifier
- The 40-qubit result: hardware 16, classical 17
- What is still required for quantum advantage?
- The 60-qubit result: hardware 17, linear 16, RBF 14
The experiment in one table
| Component | Value |
|---|---|
| Dataset | PBMC68k / Zheng68k |
| Full input per cell | 32,738 genes |
| Binary task | regulatory CD4 T cell versus CD4 memory T cell |
| Pilot | 32 training and 32 test cells |
| Quantum representation | 60 label-free coexpression modules, 4 statistical blocks |
| Hardware | IBM Fez through Fire Opal |
| Circuits | 192 circuits, 128 shots per circuit |
| Circuit | 60 qubits, logical depth 20, 134 two-qubit interactions |
| Readout | 627 Pauli observables per cell |
| 60q hardware test | 0.53125 — 17 of 32 correct |
| Linear test | 0.50000 — 16 of 32 correct |
| RBF test | 0.43750 — 14 of 32 correct |
| Quantum time reported by the Fire Opal dashboard | 26 seconds |
| Submission to retrieval | about 8 minutes 33 seconds |
| Classical MPS attempt | stopped after 42 minutes 57 seconds without a converged reference |
| Historical ratio against unfinished MPS (not evidence of advantage) | greater than 99.1x at kernel scope; greater than 5.0x including retrieval |
Which components are literal QOS?
| Route | Relationship to the QOS paper |
|---|---|
| 4q flat-QOS toy/pilot | Literal port of the official q_state_sketch_flat sampling kernel for \(D=16\) and \(M=64\); 66 circuits on IBM Fez, Fire Opal action 2334156; mean Hellinger fidelity 0.990104 over 64 random kernels |
| 40q/60q PBMC68k | QOS-inspired hardware feature maps using classically computed rotation angles and Pauli readout; no literal sampling oracle, QSVT or classical-shadow chain |
| Complete paper route | Streaming sample access, oracle construction, quantum linear algebra and controlled readout; not implemented end to end on hardware in this project |
The 4q run therefore shows that a genuine QOS sketch building block works on hardware. The 60q run shows something different: a wide, shallow and biologically structured feature map for real PBMC68k data is executable and reaches an interesting local timing and point score. Neither result by itself is a hardware proof of Theorem 3.
What this series does and does not claim
The execution shows that the complete route—from real single-cell RNA data, through label-free gene modules and a compact quantum feature map, to measured hardware features and a predeclared classifier—is technically executable. The 60-qubit route also had the best held-out point score of the three preselected models.
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.
That is exactly why the series is useful. It explains not only how the theory works, but also where the difficult transition to real hardware lies: data access, circuit depth, readout, shot noise, generalisation, and a fair classical comparison.