Physics Commons^™

Connecting Ansatz Expressibility To Gradient Magnitudes And Barren Plateaus, Zoe Holmes, Kunal Sharma, M Cerezo, Patrick Coles

Faculty Publications

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 …