Benchmarking bosonic modes for quantum information with randomized displacements

TL;DR

This paper introduces a bosonic randomized benchmarking protocol using phase space displacements to assess quantum mode quality, analyze error effects, and experimentally validate the approach with trapped ions.

Contribution

It presents a novel bosonic benchmarking method based on randomized displacements, enabling efficient error characterization in quantum information systems.

Findings

The protocol accurately identifies error processes like heating and dephasing.

Experimental validation shows good agreement with theoretical models.

Highly correlated dephasing noise is identified as the dominant error source.

Abstract

Bosonic modes are prevalent in all aspects of quantum information processing. However, existing tools for characterizing the quality, stability, and noise properties of bosonic modes are limited, especially in a driven setting. Here, we propose, demonstrate, and analyze a bosonic randomized benchmarking (BRB) protocol that uses randomized displacements of the bosonic modes in phase space to determine their quality. We investigate the impact of common analytic error models, such as heating and dephasing, on the distribution of outcomes over randomized displacement trajectories in phase space. We show that analyzing the distinctive behavior of the mean and variance of this distribution - describable as a gamma distribution - enables identification of error processes, and quantitative extraction of error rates and correlations using a minimal number of measurements. We experimentally validate the analytical models by injecting engineered noise into the motional mode of a trapped ion system and performing the bosonic randomized benchmarking protocol, showing good agreement between experiment and theory. Finally, we investigate the intrinsic error properties in our system, identifying the presence of highly correlated dephasing noise as the dominant process.