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Quantum algorithms for Noisy Intermediate-Scale Quantum (NISQ) machines haverecently emerged as new promising routes towards demonstrating near-termquantum advantage (or supremacy) over classical systems. In these systemssamples are typically drawn from probability distributions which --- underplausible complexity-theoretic conjectures --- cannot be efficiently generatedclassically. Rather than first define a physical system and then determinecomputational features of the output state, we ask the converse question: givendirect access to the quantum state, what features of the generating system canwe efficiently learn? In this work we introduce the Variational QuantumUnsampling (VQU) protocol, a nonlinear quantum neural network approach forverification and inference of near-term quantum circuits outputs. In ourapproach one can variationally train a quantum operation to unravel the actionof an unknown unitary on a known input state; essentially learning the inverseof the black-box quantum dynamics. While the principle of our approach isplatform independent, its implementation will depend on the unique architectureof a specific quantum processor. Here, we experimentally demonstrate the VQUprotocol on a quantum photonic processor. Alongside quantum verification, ourprotocol has broad applications; including optimal quantum measurement andtomography, quantum sensing and imaging, and ansatz validation.

Variational Quantum Unsampling on a Quantum Photonic Processor