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

The notion of universal quantum computation can be generalized to multilevel 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 generalization of the Molmer-Sorensen gate for two-qudit gates, and a measurement scheme which utilizes shelving to a metastable 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 Ba-137(+) 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.

通用量子计算的概念可以推广到多能级量子比特（qudit），这在资源利用和算法效率方面具有优势。囚禁离子作为纯净且易于精确控制的量子系统，为开发基于量子比特的量子信息处理提供了理想平台。此前的研究尚未充分探究在考虑已知实验误差源的情况下实现囚禁离子量子比特的可行性。在此，我们阐述了一套通用的协议，涵盖态制备、单量子比特门、针对双量子比特门的莫尔默 - 索伦森门（Molmer - Sorensen gate）的推广，以及一种利用将粒子转移至亚稳能级的测量方案。我们对以往囚禁离子实验中的已知误差源进行了数值模拟，结果表明，对于在钡 - 137（+）离子中编码的三能级量子比特，实现保真度高于99%不存在根本性限制。我们的方法可扩展至更高维度的量子比特，并且我们的测量和单量子比特门协议对于五能级量子比特可实现99%的保真度。我们还指明了在未来工作中进一步降低误差的途径。我们的研究结果表明，三能级囚禁离子量子比特将成为量子信息处理领域一项有用的技术。