Realistic high-fidelity protocols for qudit-based quantum computing

We present on the feasibility of implementing quantum information processing using multi-level qudits encoded within trapped ions. We describe protocols for how current technology may be used to implement high-fidelity state preparation, measurement, and single- and two-qudit gates in a trapped ion framework. A scalable measurement scheme using rapid adiabatic passage to a meta-stable state is presented, along with a discussion of single-qudit gate implementation, and a practical method for implementing two-qudit entangling gates (mediated by collective phonon modes) using a geometric phase approach. From our error estimations, we can achieve better than 99% fidelity for three- and five-level qudit operations and measurement, which will allow us to perform fault-tolerant quantum computing on these platforms. We anticipate that further improvements to the measurement technique and the qudit manipulations could be made to push these fidelities higher.