The simulation works. The hardware doesn't. Predict the gap before you run.
Variational Quantum Classifiers on noisy hardware (arXiv:2603.21300): models trained and validated in noiseless simulation frequently fail when deployed on actual quantum devices. The performance gap — simulation accuracy minus hardware accuracy — varies wildly across circuits, datasets, and devices. No simple predictor existed.
The finding: the average relative entropy difference between classes, combined with transpilation circuit depth, strongly correlates with the simulation-to-hardware performance gap. High class separation (large relative entropy difference) and shallow circuits (low transpilation depth) predict noise robustness. Low class separation and deep circuits predict failure.
Circuit depth alone fails for shallow circuits — a common regime for near-term quantum computing. Two circuits with the same depth can have very different noise robustness depending on how separated the classes are in the quantum state space. The entropy metric captures what depth misses: how much “room” the classification has for noise before the decision boundary is crossed.
Validated across diverse VQC implementations, multiple datasets, and multiple quantum devices. The metric is practical: compute it from the simulation (which is cheap) to predict whether the hardware deployment (which is expensive and limited) will succeed.
The structural insight: the transferability from simulation to hardware depends on two things — how robust the signal is (class separation) and how much noise the circuit accumulates (depth). Both matter; neither alone suffices. A well-separated classification on a deep circuit may fail (too much noise). A poorly separated classification on a shallow circuit may also fail (too little signal). The metric captures their interaction: signal-to-noise ratio for quantum classifiers.