Abstract
Bayesian methods in machine learning, such as Gaussian processes, have great advantages compared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to deep architectures has remained a major challenge. Recent results connected deep feedforward neural networks with Gaussian processes, allowing training without backpropagation. This connection enables us to leverage a quantum algorithm designed for Gaussian processes and develop a new algorithm for Bayesian deep learning on quantum computers. The properties of the kernel matrix in the Gaussian process ensure the efficient execution of the core component of the protocol, quantum matrix inversion, providing at least a polynomial speedup over classical algorithms. Furthermore, we demonstrate the execution of the algorithm on contemporary quantum computers and analyze its robustness with respect to realistic noise models.
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Notes
Information about performance measures of Rigetti’s QPUs can be found in http://docs.rigetti.com/en/1.9/qpu.html.
Information about performance measures of IBM’s QPUs can be found in http://www.research.ibm.com/ibm-q/technology/devices/.
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Acknowledgements
We would like to thank Piotr Gawron (Polish Academy of Sciences), Will Zeng and Ryan Karle (Rigetti Computing), and Joseph Fitzsimons (SUTD and CQT) for discussions.
Funding
Z. Z. received support from Singapore’s Ministry of Education and National Research Foundation under NRF Award NRF-NRFF2013-01. The work of A. P.-K. is supported by Fundación Obra Social “la Caixa” (LCF/BQ/ES15/10360001), the Spanish MINECO (QIBEQI FIS2016-80773-P and Severo Ochoa SEV-2015-0522), Fundació Privada Cellex, and the Generalitat de Catalunya (SGR1381 and CERCA Program). This research was supported by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation.
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Zhao, Z., Pozas-Kerstjens, A., Rebentrost, P. et al. Bayesian deep learning on a quantum computer. Quantum Mach. Intell. 1, 41–51 (2019). https://doi.org/10.1007/s42484-019-00004-7
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DOI: https://doi.org/10.1007/s42484-019-00004-7