Fidelity measurement of a multiqubit cluster state with minimal effort

TL;DR

This paper introduces a scalable, efficient method for experimentally estimating the fidelity of multiqubit cluster states, significantly reducing measurement complexity while accurately accounting for typical experimental errors.

Contribution

The authors propose a physically-motivated fidelity measurement method that scales linearly with system size, providing tight bounds for realistic noise in multiqubit cluster states.

Findings

Method yields a lower bound with linear measurement scaling.

Accurately accounts for most relevant experimental errors.

Performs well for higher-dimensional cluster states.

Abstract

The size of the Hilbert space for a multiqubit state scales exponentially with the number of constituent qubits. Often this leads to a similar exponential scaling of the experimental resources required to characterize the state. Contrary to this, we propose a physically-motivated method for experimentally assessing the fidelity of an important class of entangled states known as cluster states. The proposed method always yields a lower bound of the fidelity with a number of measurement settings scaling only linearly with the system size, and is tailored to correctly account for the errors most likely to occur in experiments. For one-dimensional cluster states, the constructed fidelity measure is tight to lowest order in the error probability for experimentally realistic noise sources and thus closely matches the true fidelity. Furthermore, it is tight for the majority of higher-order errors, except for a small subset of certain non-local multiqubit errors irrelevant in typical experimental situations. The scheme also performs very well for higher-dimensional cluster states, including correctly the majority of experimentally relevant errors.