Quantum process tomography of a M{\o}lmer-S{\o}rensen gate via a global beam

TL;DR

This paper introduces a practical framework for quantum process tomography of two-ion gates using a global laser beam, enabling detailed error analysis and improved characterization of entangling gates in trapped-ion quantum systems.

Contribution

It presents a novel method combining trap potential modulation and composite pulses for efficient two-ion process tomography with global addressing.

Findings

Effective characterization of Mølmer-Sørensen gates

Identification of dominant error sources like laser decoherence

Comparison of optimized and overpowered gate performance

Abstract

We present a framework for quantum process tomography of two-ion interactions that leverages modulations of the trapping potential and composite pulses from a global laser beam to achieve individual-ion addressing. Tomographic analysis of identity and delay processes reveals dominant error contributions from laser decoherence and slow qubit frequency drift during the tomography experiment. We use this framework on two co-trapped $^{40}$Ca$^+$ ions to analyze both an optimized and an overpowered M{\o}lmer-S{\o}rensen gate and to compare the results of this analysis to a less informative Bell-state tomography measurement and to predictions based on a simplified noise model. These results show that the technique is effective for the characterization of two-ion quantum processes and for the extraction of meaningful information about the errors present in the system. The experimental convenience of this method will allow for more widespread use of process tomography for characterizing entangling gates in trapped-ion systems.