Barren Plateaus as Destructive Interference: A Diagnostic Framework and Implications for Structured Ansatzes

TL;DR

This paper introduces a diagnostic framework to understand barren plateaus in quantum neural networks as destructive interference among gradient contributions, revealing differences between ansatzes and connecting to variance-based theories.

Contribution

It presents a new interference-based perspective on barren plateaus, with diagnostic tools and analysis of different ansatzes, linking destructive interference to gradient suppression mechanisms.

Findings

Haar-random sign cancellation regime identified with stable interference measure

HEA remains near the random-sign cancellation regime across sizes and depths

HVA shows larger interference measures due to sign organization, not just term count

Abstract

Barren plateaus (BPs) are usually described by the exponential suppression of gradient variance, but the mechanism by which gradient signal disappears remains unclear. We show that this phenomenon can be understood as destructive interference among termwise gradient contributions. To make this perspective operational, we introduce a diagnostic framework based on the cancellation ratio $R_k$, the effective term count $N_{\mathrm{eff},k}$, and the interference-quality measure $B_{\mathrm{eff},k}=R_k\sqrt{N_{\mathrm{eff},k}}$. Under a random-sign model, $B_{\mathrm{eff},k}$ remains near a stable baseline, defining a random-sign cancellation regime. For the transverse-field Ising model (TFIM), we find that the hardware-efficient ansatz (HEA) remains close to this regime across system sizes and depths, whereas the Hamiltonian variational ansatz (HVA) systematically escapes it. In particular, HVA exhibits larger $B_{\mathrm{eff},k}$ not merely because $N_{\mathrm{eff},k}$ is larger, but because $R_k$ also remains systematically larger despite the broader term participation. This pattern indicates improved sign organization rather than simple term suppression. We further establish an exact identity that connects the proposed interference diagnostics directly to the standard variance-based theory of BPs. These results position destructive interference as a mechanistic interpretation of BP-like behavior in the regimes studied here, but they do not imply that BPs and destructive interference are universally interchangeable across all architectures and settings.