Variational Quantum Unsampling on an Photonic Quantum Processor*

Quantum algorithms for Noisy Intermediate-Scale Quantum (NISQ) processors have emerged as promising routes towards demonstrating practical advantage over classical machines. In these systems samples are typically drawn from probability distributions which — under plausible complexity-theoretic conjectures — cannot be efficiently generated classically. Rather than first define a physical system and then determine computational features of the output state, we ask the converse question: given direct access to the quantum state, what features of the generating system can we efficiently learn? Here, we introduce the Variational Quantum Unsampling (VQU) protocol, a nonlinear quantum neural network approach for verification and inference of near-term quantum circuits outputs. We experimentally demonstrate this 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.