Within this project, we developed a universal toolbox for qudit quantum information processing with trapped ions. This includes arbitrary pairwise addressed two-level entangling operations in a standardized form that is flexibly embedded in qudit Hilbert spaces of arbitrary (also mixed) dimension. We benchmarked the performance of this toolbox to confirm that it does not notably degrade with dimension, beyond what would be expected due to the higher number of laser pulses required compared to operating the same device as a standard qubit quantum processor. Further enhancing this toolbox, we developed and demonstrated a genuine qudit entangling operation, which enables the direct creation of entanglement over the whole qudit Hilbert space in one gate application. This gate mechanism comes with less control overhead, independent of the qudit dimension, increased performance, and higher entangling power than standard embedded two-level couplings. Together these gates form a powerful toolbox for qudit quantum information processing in trapped ions.
Using the developed methods, we performed a quantum simulation of a topological quantum spin system, where neighboring spins were encoded in distinct subspaces of the qudit Hilbert space. This resulted in almost complete suppression of cross-talk errors, enabling us to perform the simulation in a trapping regime that would not have otherwise been possible and significantly boosting the performance of the quantum processor.
We further exploited the newly developed capabilities to achieve single-setting quantum state characterization by implementing symmetric informationally-complete (SIC) positive operator-valued measures (POVM). The four-outcome SIC POVM is known to be the optimal local measurement for a qubit, yet being non-projective it cannot be realized directly in practice. We demonstrate, how to embed a qubit locally into a four-level system in a way that this measurement turns projective. As a result, the complete characterization of a multi-qubit system, which typically requires an exponential number of measurement settings becomes possible with just a single fixed measurement setting, regardless of the system size, and with virtually no experimental overhead. In addition, we developed a SIC POVM extension of the classical shadow framework, enabling highly efficient data processing for SIC POVMs. Together, these techniques enable, as we demonstrated, the characterization of linear and nonlinear properties of multi-qubit quantum systems in an online fashion.
In summary, we developed and demonstrated a complete toolkit for qudit quantum information processing. As a first application, we already demonstrated how this platform enables a paradigm shift in the way qubit systems can be characterized, and we made first steps towards using it for quantum simulation applications. Over the course of the project, the fellow co-authored 12 publications (4 published, 8 currently under review) and presented the project results at 8 international conferences and workshops (5 invited). The fellow also initiated fruitful and ongoing collaborations with several European and international research groups and made several contributions to outreach events, including as a finalist in Falling Walls Emerging Talents.
