# Certification of continuous-variable gates using average channel-fidelity witnesses

## TL;DR

This paper develops practical, Gaussian-measurement-based witnesses for certifying the fidelity of continuous-variable quantum gates, including Gaussian and non-Gaussian types, with applications in validating quantum technologies.

## Contribution

It introduces a broad framework for certifying continuous-variable quantum gates using average channel-fidelity witnesses that are experimentally feasible and efficient.

## Key findings

- Witnesses provide tight lower bounds on fidelity.
- Method applies efficiently to multiple modes and non-Gaussian gates.
- Improved measurement scheme enhances efficiency for Gaussian states.

## Abstract

We introduce witnesses for the average channel fidelity between a known target gate and an arbitrary unknown channel, for continuous-variable (CV) systems. These are observables whose expectation value yields a tight lower bound to the average channel fidelity in question, thus constituting a practical tool for certification of experimental CV gates. Our framework applies to a broad class of target gates. Here, we focus on three specific types of targets: multi-mode Gaussian unitary channels, single-mode coherent state amplifiers, and the single-mode (non-Gaussian) cubic phase gate, which is a crucial ingredient for CV universal quantum computation. Our witnesses are experimentally-friendly as they rely exclusively on Gaussian measurements, even for the non-Gaussian-target case. Moreover, in all three cases, they can be measured efficiently in the estimation error $\epsilon$ and failure probability $\Delta$, as well as in the number of modes $m$ for the Gaussian-target case. To end up with, our approach for the Gaussian-target case relies on an improved measurement scheme for Gaussian state-fidelity witnesses, which is polynomially and exponentially more efficient in $m$ and $\Delta$, respectively, than previous schemes. The latter constitutes an interesting byproduct result on its own. Our findings are relevant to the experimental validation of many-body quantum technologies.