Details

Autor(en) / Beteiligte

• Uvarov, A V
• Biamonte, J D

Titel

On barren plateaus and cost function locality in variational quantum algorithms

Ist Teil von

• Journal of physics. A, Mathematical and theoretical, 2021-06, Vol.54 (24), p.245301

Ort / Verlag

IOP Publishing

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.