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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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.
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.
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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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