# Practical trapped-ion protocols for universal qudit-based quantum computing

## TL;DR

This paper develops practical protocols for universal quantum computing using trapped-ion qudits, demonstrating high-fidelity operations for three- and five-level systems through numerical simulations.

## Contribution

It introduces a comprehensive set of protocols for state preparation, gates, and measurement of trapped-ion qudits, extending to higher dimensions with high fidelity.

## Key findings

- Fidelities above 99% achievable for three-level qudits in Ba+ ions
- Protocols extend to five-level qudits with 99% fidelity
- Numerical simulations show no fundamental limitations for high-fidelity operations

## Abstract

The notion of universal quantum computation can be generalized to multi-level qudits, which offer advantages in resource usage and algorithmic efficiencies. Trapped ions, which are pristine and well-controlled quantum systems, offer an ideal platform to develop qudit-based quantum information processing. Previous work has not fully explored the practicality of implementing trapped-ion qudits accounting for known experimental error sources. Here, we describe a universal set of protocols for state preparation, single-qudit gates, a new generalization of the M\o{}lmer-S\o{}rensen gate for two-qudit gates, and a measurement scheme which utilizes shelving to a meta-stable state. We numerically simulate known sources of error from previous trapped ion experiments, and show that there are no fundamental limitations to achieving fidelities above \(99\%\) for three-level qudits encoded in \(^{137}\mathrm{Ba}^+\) ions. Our methods are extensible to higher-dimensional qudits, and our measurement and single-qudit gate protocols can achieve \(99\%\) fidelities for five-level qudits. We identify avenues to further decrease errors in future work. Our results suggest that three-level trapped ion qudits will be a useful technology for quantum information processing.