Error-mitigated inference of quantum network topology

TL;DR

This paper introduces a scalable method to determine the topology and quantify entanglement in unknown quantum networks using minimal local measurements, enhanced by error mitigation techniques for practical robustness.

Contribution

It presents a novel approach combining entropic uncertainty and mutual information with error mitigation to efficiently reveal network topology and entanglement.

Findings

PEC removes deviations in correlation estimates

VD extends noise tolerance for entanglement certification

Method applicable across various quantum platforms

Abstract

Paramount for performances of quantum network applications are the structure and quality of distributed entanglement. Here we propose a scalable and efficient approach to reveal the topological information of unknown quantum networks, and quantify entanglement simultaneously. The scheme exploits entropic uncertainty, an operationally meaningful measure of correlation, by performing only two local measurements on each qubit. Moreover, when measurement outcomes in each node are collectively evaluated, integrating uncertainty and mutual information enables a direct count of the number of bipartite sources between any two nodes. This surpasses what is possible via applying either approach solely. Moreover, quantum error mitigation techniques including probabilistic error cancellation (PEC) and virtual distillation (VD), which have been widely applied to suppress biases in single expectation value, are further incorporated to mitigate errors in entropic quantities. We find that PEC successfully removes deviations in correlation estimations. Meanwhile, VD extends the depolarizing noise strength that allows for valid bipartite entanglement certification from 8.8% to 26.4%, thus substantially enhancing robustness against bias-inducing noise in practical situations. The proposal is applicable to a broad variety of platforms and helps to spur future studies toward harnessing the advantages of quantum networks.