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# Variational quantum unsampling on a quantum photonic processor

### Subjects

An Author Correction to this article was published on 04 February 2020

## Abstract

A promising route towards the demonstration of near-term quantum advantage (or supremacy) over classical systems relies on running tailored quantum algorithms on noisy intermediate-scale quantum machines. These algorithms typically involve sampling from probability distributions that—under plausible complexity-theoretic conjectures—cannot be efficiently generated classically. Rather than determining the computational features of output states produced by a given physical system, we investigate what features of the generating system can be efficiently learnt given direct access to an output state. To tackle this question, here we introduce the variational quantum unsampling protocol, a nonlinear quantum neural network approach for verification and inference of near-term quantum circuit outputs. In our approach, one can variationally train a quantum operation to unravel the action of an unknown unitary on a known input state, essentially learning the inverse of the black-box quantum dynamics. While the principle of our approach is platform independent, its implementation will depend on the unique architecture of a specific quantum processor. We experimentally demonstrate the variational quantum unsampling protocol on a quantum photonic processor. Alongside quantum verification, our protocol has broad applications, including optimal quantum measurement and tomography, quantum sensing and imaging, and ansatz validation.

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## Data availability

The datasets generated during and or analysed during the current study are available from the corresponding author on reasonable request.

## Change history

• ### 04 February 2020

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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## Acknowledgements

We thank E. Farhi, E. Grant, D. Hangleiter, I. Marvian, J. McClean, M. Pant, M. Schuld, P. Shadbolt, S. Sim and G. Steinbrecher for insightful discussions. This work was supported by the AFOSR MURI for Optimal Measurements for Scalable Quantum Technologies (FA9550-14-1-0052), the MITRE Quantum Moonshot Program and by the AFOSR programme FA9550-16-1-0391, supervised by G. Pomrenke. J.C. is supported by EU H2020 Marie Sklodowska-Curie grant number 751016.

## Author information

Authors

### Contributions

J.C., M.M., S.L. and D.E. conceived the project. J.C., M.M., J.P.O., M.Y.N, S.L. and D.E. developed the theory. J.C., M.P., C.C., D.B., N.C.H., F.N.C.W., M.H. and D.E. contributed to the experimental set-up. J.C., M.P., C.C. and D.B. performed the experiment and analysed data. J.C. performed numerical experiments. All authors contributed to the discussion of the results and the writing of the manuscript.

### Corresponding author

Correspondence to Jacques Carolan.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–4 and Sections I–V.

## Rights and permissions

Reprints and Permissions

Carolan, J., Mohseni, M., Olson, J.P. et al. Variational quantum unsampling on a quantum photonic processor. Nat. Phys. 16, 322–327 (2020). https://doi.org/10.1038/s41567-019-0747-6

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