Why is the VQE insensitive to noise?

Question

I was going through the Grove documentation on the Variational Quantum Eigensolver. In one of the demonstrations with noisy gates, it is seen that resulting eigenvalue is quite close to the expected result, at least until the noise level exceeds a threshold. Is there a mathematical calculation which shows why the VQE is relatively insensitive to the low-level noise, and can the "threshold" (if it is indeed a threshold) be calculated for different ansätze?

KAJ226 · Answer

I think it is similar to how Neural Networks are also good at handling noise (up to a certain threshold).
VQE uses parameterized quantum circuit and hence it has the ability to adjust its parameters to absorb some of the noise. This is like how neural networks adjust their weights to absorb noise in the training data.

Why is the VQE insensitive to noise?

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