The Average Relative Entropy and Transpilation Depth determines the noise robustness in Variational Quantum Classifiers

The extensive empirical evaluation is the paper's primary strength, covering over 8,500 trained models across 20+ ansatz structures, five dataset types, and multiple noisy backends. The central observation—that depth alone fails to predict noise resilience—is convincingly demonstrated: as noted in Section VI, "a circuit with a depth of 2033 showed a higher accuracy difference of 0.4... while another circuit with a depth of 2236 exhibited a much smaller accuracy difference of just 0.029." The proposed log-DTSAE metric ($\log(\text{depth}/\sqrt{D_{avg}})$) effectively stratifies model performance, and the authors honestly report negative results, noting that "No model with low accuracy difference... was observed for Amplitude encoding."

The study relies predominantly on simulated "fake" backends, with real hardware validation limited to constrained experiments on IBM and IQM devices due to cost barriers. The Average Relative Entropy $D_{avg}(\rho||\sigma) = \frac{1}{n+m}\sum_{i,j} D(U\rho_i U^\dagger||U\sigma_j U^\dagger)$ requires $\mathcal{O}(nm)$ pairwise quantum state tomography or simulation costs, becoming prohibitive for large test sets. Furthermore, while claiming evaluation "without explicit executions on quantum devices," the method requires prior knowledge of the specific device's transpilation depth and gate set, which may not be available a priori. The threshold values (e.g., log-DTSAE < 3.5) appear empirically fitted to simulated noise models rather than theoretically derived, raising questions about their validity under real hardware temporal drift.

The evidence robustly supports the claim that combining entropy with depth improves prediction over either factor individually, as shown in Table I where models with similar depths diverge significantly based on entropy values. The comparison to prior work is generally fair, particularly challenging Sharma et al.'s claims of depth-independent resilience with the observation that "circuit depth alone is insufficient to characterize shallow circuits." However, the contradiction of Ahmed et al.'s probability distribution hypothesis lacks quantitative statistical analysis. The diversity of experimental controls—20+ ansatzes, multiple optimizers (Adam, AdaGrad, etc.), and five distinct dataset generators—strengthens generalizability claims, though the >85% accuracy threshold for model selection may introduce survivorship bias toward well-behaved circuits.

The authors provide GitHub repositories for training, testing, and analysis code with specific commit references from March 2026. Experimental components are well-documented, including standard dataset generators (Make Classification, Hidden Manifold, Hyperplanes, Two Curves) and explicit ansatz definitions (QNN pooling, Data Re-upload). However, specific training hyperparameters (learning rates, batch sizes, convergence thresholds) are described only generally as "varying" rather than tabulated exhaustively. The transpilation depth calculations depend on Qiskit's transpiler version and optimization settings (not explicitly specified), which significantly affect quantum circuit depth. While the code appears complete, the computational requirements (8,500+ models trained on the Puhti Supercomputer) present a substantial barrier to independent verification. Limited validation on actual quantum devices (Fez, Torino, Marrakesh, Emerald) versus extensive simulations leaves open questions about threshold validity under real temporal noise fluctuations.