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

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Abstract

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) toward 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.

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Data availability

Raw data for this study were generated by running quantum circuits via QISKIT on real quantum processors IBM Athens and Bogota or simulator. The datasets generated during the current study are available from the corresponding author on request.

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Acknowledgements

We acknowledge use of the IBM Quantum Experience for this work. The viewpoints expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum Experience team. A. A. Zh. acknowledges a support from RFBR (project no. 20-37-70028). W. V. P. acknowledges a support from RFBR (project no. 19-02-00421).

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Authors and Affiliations

  1. Dukhov Research Institute of Automatics (VNIIA), Moscow, 127055, Russia

    Andrey Zhukov & Walter Pogosov

  2. Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Moscow, 125412, Russia

    Walter Pogosov

  3. HSE University, Moscow, 109028, Russia

    Walter Pogosov

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  1. Andrey Zhukov
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  2. Walter Pogosov
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Zhukov, A., Pogosov, W. Quantum error reduction with deep neural network applied at the post-processing stage. Quantum Inf Process 21, 93 (2022). https://doi.org/10.1007/s11128-022-03433-9

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