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.
Highlights
In current approaches to developing quantum computing hardware, each constituent building block, such as a trapped ion, superconducting resonator, etc., is typically used to encode a two-level qubit
The straightforward methods we describe are directly generalized from current ion trap qubit techniques, and so are intuitive to implement for experimentalists already working with ion qubits
Work by Andrist et al [46] and Campbell et al [44,45] indicates that the error thresholds to successfully implement error correction increase with the number of qudit levels, implying that fault-tolerant quantum computing for qudits may be able to sustain a higher error rate
Summary
In current approaches to developing quantum computing hardware, each constituent building block, such as a trapped ion, superconducting resonator, etc., is typically used to encode a two-level qubit. To determine whether qudit-based quantum processors could be more scalable than qubit-based processors, several lines of inquiry are needed One, it must be determined whether idealized qudits offer advantages over idealized qubits; two, it must be shown that the necessary qudit operations can be practically achieved in experiments; and three, it must be investigated whether the advantages offered by idealized qudits are outweighed by tradeoffs with increased experimental complexity and more potential sources of error. Work by Andrist et al [46] and Campbell et al [44,45] indicates that the error thresholds to successfully implement error correction increase with the number of qudit levels, implying that fault-tolerant quantum computing for qudits may be able to sustain a higher error rate. Environmental noises are, considered difficult to be removed, and are included in our assessment
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