in Variational Quantum Circuits
Noise accumulation limits the performance of variational quantum circuits in the noisy intermediate-scale quantum (NISQ) regime. Standard analyses typically rely on global distributional metrics, such as total variation distance (TVD) over full measurement outputs. However, in highly expressive or scrambling circuits, global TVD often saturates and becomes insensitive to structural differences between ansatz families. In this work we show that local entropy provides a universal control parameter for local noise sensitivity under depolarizing noise. We prove that the marginal TVD of one-qubit and two-qubit subsystems is upper-bounded by a function of the entropic deficit from maximal mixing. We then demonstrate numerically that scrambling circuits exhibit entropic self-averaging, leading to a universal collapse of local TVD when plotted against mean single-qubit entropy. Furthermore, we identify the ratio between two-local and one-local sensitivities as a structural marker of scrambling dynamics. These results establish local entropy as a principled and architecture-independent predictor of measurement-level noise response.
Keywords: local entropy, noise sensitivity, variational quantum circuits, depolarizing noise, marginal total variation distance