From coherence to mixedness: a driver of barren plateaus in variational quantum algorithms

Abstract

Variational quantum algorithms (VQAs) are a leading approach for near-term quantum advantage. However, their training is often hindered by barren plateaus (BPs). We present a framework based on observational entropy. The framework separates the coherent part of a quantum state from its incoherent part. We define the coherence fraction $\eta$ as the ratio of coherent to total contribution. This quantity measures how much of the coherence capacity is in a usable form. Using a 4-qubit Ising model and a hardware-efficient ansatz, we show that $\eta$ decreases monotonically during optimization, while the coherence capacity remains nearly constant. Our results show that $\eta$ provides an early indication of gradient collapse. It outperforms conventional diagnostics such as the gradient norm and entanglement entropy. This work offers a resource-theoretic explanation for BPs. It also provides a basis for real-time monitoring of coherence loss on noisy devices.

36 pages, 10 figures,6 tables