Quantum error reduction with deep neural network applied at the
  post-processing stage
Deep neural networks (DNN) can be applied at the post-processing stage for
the improvement of the results of quantum computations on noisy
intermediate-scale quantum (NISQ) processors. Here, we propose a method based
on this idea, which is most suitable for digital quantum simulation
characterized by the periodic structure of quantum circuits consisting of
Trotter steps. A key ingredient of our approach is that it does not require any
data from a classical simulator at the training stage. The network is trained
to transform data obtained from quantum hardware with artificially increased
Trotter steps number (noise level) towards the data obtained without such an
increase. The additional Trotter steps are fictitious, i.e., they contain
negligibly small rotations and, in the absence of hardware imperfections,
reduce essentially to the identity gates. This preserves, at the training
stage, information about relevant quantum circuit features. Two particular
examples are considered that are the dynamics of the transverse-field Ising
chain and XY spin chain, which were implemented on two real five-qubit IBM Q
processors. A significant error reduction is demonstrated as a result of the
DNN application that allows us to effectively increase quantum circuit depth in
terms of Trotter steps.
A. A. Zhukov W. V. Pogosov