Abstract: A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective talk, 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 present a case-by-case argument that commonly used models with provable absence of barren plateaus are also in a sense classically simulable, 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. We end by discussing 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.
Bio: Zoë Holmes received in 2015 her MPhil degree in Physics and Philosophy from the University of Oxford. In 2016 she obtained her MRes (Master of Research) from the Imperial College London, where in 2019 she got her PhD in quantum thermodynamics. In 2020 she started as a Postdoctoral Researcher at Los Alamos National Laboratory (USA) working on quantum algorithms and quantum machine learning methods for Noisy Intermediate-Scale Quantum (NISQ) computers. In 2021 she became the Mark Kac Fellow at Los Alamos National Lab. Since August 2022 she is Tenure Track Assistant Professor of Physics at EPFL.