On barren plateaus and cost function locality in variational quantum algorithms
This work clarifies the conditions for barren plateaus, a critical challenge for researchers developing and optimizing variational quantum algorithms.
This paper investigates the phenomenon of barren plateaus in variational quantum algorithms, where gradients vanish exponentially. The authors derive a lower bound on the gradient variance, showing its dependence on the causal cone width of each term in the cost function's Pauli decomposition.
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.