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We present optimized distillation schemes for preparingGreenberger-Horne-Zeilinger (GHZ) states. Our approach relies on trainingvariational quantum circuits with white noise affected GHZ states as inputs.Optimizing for a single iteration of the scheme, we find that it is possible toachieve an increased fidelity to the GHZ state, although further iterationsdecrease the fidelity. The same scheme, acting on coherently distortedpure-state inputs, is effective only in certain special cases. We show thatradically different results can be achieved, however, when one optimizes forthe output after two iterations of the protocol. In this case, the obtainedschemes are more effective in distilling GHZ states from inputs affected bywhite noise. Moreover, they can also correct several types of coherentpure-state errors.

Training iterated protocols for distillation of GHZ states with variational quantum algorithms