Avoiding barren plateaus in the variational determination of geometric
  entanglement
The barren plateau phenomenon is one of the main obstacles to implementing
variational quantum algorithms in the current generation of quantum processors.
Here, we introduce a method capable of avoiding the barren plateau phenomenon
in the variational determination of the geometric measure of entanglement for a
large number of qubits. The method is based on measuring compatible two-qubit
local functions whose optimization allows for achieving a well-suited initial
condition, from which a global function can be further optimized without
encountering a barren plateau. We analytically demonstrate that the local
functions can be efficiently estimated and optimized. Numerical simulations up
to 18-qubit GHZ and W states demonstrate that the method converges to the exact
value. In particular, the method allows for escaping from barren plateaus
induced by hardware noise or global functions defined on high-dimensional
systems. Numerical simulations with noise are in agreement with experiments
carried out on IBM's quantum processors for 7 qubits.
Leonardo Zambrano Andrés Damián Muñoz-Moller Mario Muñoz Luciano Pereira Aldo Delgado