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Deep neural networks (DNN) can be applied at the post-processing stage forthe improvement of the results of quantum computations on noisyintermediate-scale quantum (NISQ) processors. Here, we propose a method basedon this idea, which is most suitable for digital quantum simulationcharacterized by the periodic structure of quantum circuits consisting ofTrotter steps. A key ingredient of our approach is that it does not require anydata from a classical simulator at the training stage. The network is trainedto transform data obtained from quantum hardware with artificially increasedTrotter steps number (noise level) towards the data obtained without such anincrease. The additional Trotter steps are fictitious, i.e., they containnegligibly small rotations and, in the absence of hardware imperfections,reduce essentially to the identity gates. This preserves, at the trainingstage, information about relevant quantum circuit features. Two particularexamples are considered that are the dynamics of the transverse-field Isingchain and XY spin chain, which were implemented on two real five-qubit IBM Qprocessors. A significant error reduction is demonstrated as a result of theDNN application that allows us to effectively increase quantum circuit depth interms of Trotter steps.

Quantum error reduction with deep neural network applied at the post-processing stage