Effect of barren plateaus on gradient-free optimization

Author:

Arrasmith Andrew1,Cerezo M.12,Czarnik Piotr1,Cincio Lukasz1,Coles Patrick J.1

Affiliation:

1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

2. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA

Abstract

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.

Funder

LANL LDRD

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

Reference55 articles.

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