QAOA-MaxCut has barren plateaus for almost all graphs
Rui Mao, Pei Yuan, Jonathan Allcock, Shengyu Zhang

TL;DR
This paper demonstrates that QAOA applied to MaxCut graphs generally suffers from barren plateaus due to exponentially large dynamical Lie algebra dimensions, impacting trainability, and introduces a fast algorithm for DLA computation.
Contribution
It provides a detailed analysis of the DLA of QAOA for MaxCut, proving exponential growth in DLA dimension for most graphs and developing a new efficient DLA computation method.
Findings
Most graphs have exponential DLA dimension, causing barren plateaus.
The variance of the QAOA loss function decreases exponentially with system size.
A new algorithm reduces DLA computation time from days to seconds.
Abstract
The QAOA has been the subject of intense study over recent years, yet the corresponding Dynamical Lie Algebra (DLA)--a key indicator of the expressivity and trainability of VQAs--remains poorly understood beyond highly symmetric instances. An exponentially scaling DLA dimension is associated with the presence of so-called barren plateaus (BP) in the optimization landscape, which renders training intractable. In this work, we investigate the DLA of QAOA applied to the canonical MaxCut, for both weighted and unweighted graphs. For weighted graphs, we show that when the weights are drawn from a continuous distribution, the DLA dimension grows as almost surely for all connected graphs except paths and cycles. In the more common unweighted setting, we show that asymptotically all but an exponentially vanishing fraction of graphs have large DLA dimension. The…
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Taxonomy
TopicsAdvanced Graph Neural Networks · Graph Theory and Algorithms · Topological and Geometric Data Analysis
