Neural network quantum state tomography in a two-qubit experiment

TL;DR

This paper evaluates neural network-based quantum state tomography methods on real two-qubit experimental data, highlighting the importance of physical constraints and the impact of assumptions on reconstruction quality.

Contribution

It benchmarks various neural network quantum state tomography approaches on actual experimental data, emphasizing the effects of physical constraints and assumptions.

Findings

Confining the variational manifold to physical states improves reconstruction quality.

Including assumptions like pure states facilitates learning but introduces bias.

Experimental imperfections significantly affect the performance of neural network tomography.

Abstract

We study the performance of efficient quantum state tomography methods based on neural network quantum states using measured data from a two-photon experiment. Machine learning inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. While the power of these methods has been demonstrated on synthetic data, applications to real experimental data remain scarce. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states, i.e. to positive semi-definite density matrices, greatly improves the quality of the reconstructed states but renders the learning procedure more demanding. Including additional, possibly unjustified, constraints, such as assuming pure states, facilitates learning, but also biases the estimator.