Equivalence of cost concentration and gradient vanishing for quantum circuits: An elementary proof in the Riemannian formulation

Understand

The optimization of quantum circuits can be hampered by a decay of average gradient amplitudes with increasing system size.

• When the decay is exponential, this is called the barren plateau problem.
• Considering explicit circuit parametrizations (in terms of rotation angles), it has been shown in Arrasmith et al., Quantum Sci.
• Technol.