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# Quantum convolutional neural networks

## Abstract

Neural network-based machine learning has recently proven successful for many complex applications ranging from image recognition to precision medicine. However, its direct application to problems in quantum physics is challenging due to the exponential complexity of many-body systems. Motivated by recent advances in realizing quantum information processors, we introduce and analyse a quantum circuit-based algorithm inspired by convolutional neural networks, a highly effective model in machine learning. Our quantum convolutional neural network (QCNN) uses only O(log(N)) variational parameters for input sizes of N qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. To explicitly illustrate its capabilities, we show that QCNNs can accurately recognize quantum states associated with a one-dimensional symmetry-protected topological phase, with performance surpassing existing approaches. We further demonstrate that QCNNs can be used to devise a quantum error correction scheme optimized for a given, unknown error model that substantially outperforms known quantum codes of comparable complexity. The potential experimental realizations and generalizations of QCNNs are also discussed.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

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## Acknowledgements

We thank I. Cirac, E. Farhi, W. W. Ho, C. Nayak, H. Pichler, J. Preskill, X. Qi, A. Vishwanath, Z. Wang and X.-G. Wen for insightful discussions. I.C. acknowledges support from the Paul and Daisy Soros Fellowship, the Alfred Spector and Rhonda Kost Fellowship of the Hertz Foundation, and the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program. S.C. acknowledges support from the Miller Institute for Basic Research in Science. This work was supported through the National Science Foundation, the Center for Ultracold Atoms, the Vannevar Bush Faculty Fellowship and Google Research Award.

## Author information

Authors

### Contributions

All authors contributed extensively to the work presented in this paper.

### Corresponding author

Correspondence to Soonwon Choi.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information: Nature Physics thanks Zohar Ringel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–4.

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Cong, I., Choi, S. & Lukin, M.D. Quantum convolutional neural networks. Nat. Phys. 15, 1273–1278 (2019). https://doi.org/10.1038/s41567-019-0648-8

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• DOI: https://doi.org/10.1038/s41567-019-0648-8

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