Explain the MNIST sensitivity effect and its absence on Fashion-MNIST

Explain why amplitude damping lowers the input sensitivity of the trained four-qubit re-uploading classifier on MNIST but produces no corresponding effect on Fashion-MNIST, and determine whether the last-layer amplitude-damping contribution accounts for this difference.

Background

The paper observes that, after training with a standardized readout, amplitude damping substantially reduces input sensitivity as circuit depth increases on MNIST, whereas the corresponding sensitivities on Fashion-MNIST do not differ significantly across noise conditions. The authors propose that the last-layer non-unital contribution to the features may explain the MNIST behavior, but they do not establish this mechanism.

Resolving this issue would clarify whether the non-unital contribution produces a general robustness mechanism or whether the observed sensitivity reduction depends on specific properties of the data distribution and encoding.

References

A candidate explanation is the effective shallowness of noisy circuits. It holds for unital and non-unital noise alike, but what survives the truncation differs: under the twirls the features contain only contributions that survive the contraction of every layer, whereas under AD they also carry the last-layer term of Eq.~eq:floor, a first harmonic of a single angle, which dominates at depth before training. We have not tested whether this term accounts for the lower sensitivity on MNIST and its absence on Fashion-MNIST.

— Zero- Versus Infinite-Temperature Damping in Variational Quantum Circuits: Feature Scale, Sampling Cost, and Frame Gauge  (2610.01466 - Nguyen et al., 1 Oct 2026) in Section 5.2, “Accuracy and input sensitivity” (also summarized in Section 6, Conclusion)

It also remains to be seen whether the effect persists for more qubits and other data, whether trained models follow the temperature dependence of the floor, and whether it survives on hardware, where damping comes with dephasing.

— Zero- Versus Infinite-Temperature Damping in Variational Quantum Circuits: Feature Scale, Sampling Cost, and Frame Gauge  (2610.01466 - Nguyen et al., 1 Oct 2026) in Section 6, Conclusion

It also remains to be seen whether the effect persists for more qubits and other data, whether trained models follow the temperature dependence of the floor, and whether it survives on hardware, where damping comes with dephasing.

— Zero- Versus Infinite-Temperature Damping in Variational Quantum Circuits: Feature Scale, Sampling Cost, and Frame Gauge  (2610.01466 - Nguyen et al., 1 Oct 2026) in Section 6, Conclusion