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Variational quantum algorithms are expected to demonstrate the advantage ofquantum computing on near-term noisy quantum computers. However, training suchvariational quantum algorithms suffers from gradient vanishing as the size ofthe algorithm increases. Previous work cannot handle the gradient vanishinginduced by the inevitable noise effects on realistic quantum hardware. In thispaper, we propose a novel training scheme to mitigate such noise-inducedgradient vanishing. We first introduce a new cost function of which thegradients are significantly augmented by employing traceless observables intruncated subspace. We then prove that the same minimum can be reached byoptimizing the original cost function with the gradients from the new costfunction. Experiments show that our new training scheme is highly effective formajor variational quantum algorithms of various tasks.

Towards Efficient Ansatz Architecture for Variational Quantum Algorithms