Understanding SGD on a Quantum Circuit

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I implemented the following circuit, a very simple circuit:

I applied the technique presented on Farhi's paper - which I am so happy people in here are talking about more and more ! - and applied to this circuit:

enter image description here

For the most part the SGD (either vanilla or Adam), it works well. However, when $\alpha$ is such that the loss value for the circuit is almost 1, the optimization gets stuck and is unable to move - as if it is on a saddle point (I think it is but I am not sure as of yet).

My question is: is this what McClean's paper refers to a barren plateaus or is it like a mistake due to SGD implementation ?

Here it is the evolution of the loss function as a function of phase parameter:

enter image description here

On further consideration: I want to add that there is some noticeable difference between ADAM and VANILLA SGD on these situations; namely Vanilla does manage to converge.

Enrique Segura

Posted 2020-03-11T19:21:42.490

Reputation: 883

3Could we, at the very least, have some references? Preferably a definition of some of the terms you’re using so that the question is as self-contained as possible? – DaftWullie – 2020-03-12T06:32:18.247

No answers