Does provable absence of barren plateaus imply classical simulability?

TL;DR

This paper explores whether quantum models that avoid barren plateaus can be efficiently simulated classically, suggesting that many such models are likely classically simulable, thus questioning their quantum advantage.

Contribution

It provides evidence that models avoiding barren plateaus may be classically simulable, linking landscape structure to classical computational feasibility.

Findings

Many barren plateau-free models admit classical simulation with initial data collection.

Barren plateaus are linked to a curse of dimensionality, enabling classical approaches.

Quantum advantage remains uncertain due to potential limitations of current models.

Abstract

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We collect evidence-on a case-by-case basis-that many commonly used models whose loss landscapes avoid barren plateaus can also admit classical simulation, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing that quantum computers can be essential for collecting data, our analysis sheds doubt on the information processing capabilities of many parametrized quantum circuits with provably barren plateau-free landscapes. We end by discussing the (many) caveats in our arguments including the limitations of average case arguments, the role of smart initializations, models that fall outside our assumptions, the potential for provably superpolynomial advantages and the possibility that, once larger devices become available, parametrized quantum circuits could heuristically outperform our analytic expectations.