On barren plateaus and cost function locality in variational quantum algorithms

A. V. Uvarov, J. D. Biamonte

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in sufficiently expressive parametrized quantum circuits. It has been established that the onset of a barren plateau regime depends on the cost function, although the particular behavior has been demonstrated only for certain classes of cost functions. Here we derive a lower bound on the variance of the gradient, which depends mainly on the width of the circuit causal cone of each term in the Pauli decomposition of the cost function. Our result further clarifies the conditions under which barren plateaus can occur.

Original languageEnglish
Article number245301
JournalJournal of Physics A: Mathematical and Theoretical
Volume54
Issue number24
DOIs
Publication statusPublished - Jun 2021

Keywords

  • barren plateaus
  • quantum algorithms
  • vanishing gradients
  • variational quantum eigensolver

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