On barren plateaus and cost function locality in variational quantum algorithms

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.

Automated summary

The text discusses variational quantum algorithms and the phenomenon of barren plateaus in parametrized quantum circuits, where gradients vanish exponentially. By deriving a lower bound on the variance of the gradient, researchers clarify the conditions under which barren plateaus can occur. The onset of a barren plateau regime is shown to depend on the cost function and the width of the circuit causal cone.