Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus

Parametrized quantum circuits serve as ansatze for solving variational problems and provide a flexible paradigm for the programming of near-term quantum computers. Ideally, such ansatze should be highly expressive, so that a close approximation of the desired solution can be accessed. On the other hand, the ansatz must also have sufficiently large gradients to allow for training. Here, we derive a fundamental relationship between these two essential properties: expressibility and trainability. This is done by extending the well-established barren plateau phenomenon, which holds for ansatze that form exact 2-designs, to arbitrary ansatze. Specifically, we calculate the variance in the cost gradient in terms of…

• UD
  U.S. Department of Energy
• OO
  Office of Science
• AS
  Advanced Scientific Computing Research
• LD
  Laboratory Directed Research and Development

  Award: 20190065DR
• LA
  Los Alamos National Laboratory