In short
On this dataset the problem was never the small quantum circuit; it was the generic way the data was squeezed down to fit it. What you feed a VQC matters more than how many qubits it has. The quantum stage itself added no advantage over the classical forest.
These contributions showed that for a VQC the bottleneck was the generic PCA reduction and not the VQC itself, for this dataset. Because the votes VQC matched the performance of the RF by itself rather than adding to it, no quantum advantage is claimed.
For quantum machine learning research
The pre-stage in front of a VQC deserves as much attention as the circuit: here, changing it moved accuracy from 0.78–0.83 to 0.99.
- A pre-encoding pipeline that uses a Random Forest’s output, and not a selection of its input features, as the VQC’s input, in two variations: grouped votes and leaf embedding.
- An extreme reduction of 262,144 hashed API-call n-gram features from a behavioural malware dataset down to 2–12 features, to match the qubit counts.
- Evidence that a 2-qubit VQC with only 10 trainable parameters outperformed PCA + VQC at every qubit count up to 12. The RF pre-stage also allows shallow angle encoding that needs no two-qubit gates; at 4 and 8 qubits the RF circuits needed 6–14 CX gates against the 24–84 PCA needed.
- A paired comparison of RF and PCA as pre-stages at equal qubit counts, over 50 splits (10 at 12 qubits) and 2–12 qubits, using Wilcoxon signed-rank tests with a Bonferroni correction, across five metrics.
For malware detection
Low-qubit VQCs are usable for malware classification when they are given a good pre-stage: a 4-qubit VQC reached 0.992 accuracy, above the linear SVM (0.974) and the RBF SVM (0.833) and level with the Random Forest alone (0.991). They are not yet better than the classical model they depend on, and every result comes from a noise-free simulation (see limitations).
Future work
- Noisy simulation and real hardware, to test whether the RF arms’ fewer CX gates lead to less degradation, with a PCA + VQC angle-encoding control.
- A classical control on the votes: a logistic regression trained on the same grouped votes, to see if the VQC adds anything over a simple linear classifier.
- More datasets, feature types and multi-class labels.
- Larger qubit counts, and the full 50 splits at 12 qubits, to see whether the gap holds and whether barren plateaus appear.
- Optimiser and circuit search: a larger budget, gradient-based optimisers, and other ansätze and feature maps.
- Timing over all splits on one machine, with the forest using all threads.
Running on real hardware is likely the most important, since using VQCs with few qubits on current hardware was the reason for this research.