Jasper Phua Sing Cheng

Quantum computational advantage is generally attributed to coherent interference and other non-classical resources, yet their respective roles remain difficult to disentangle in experimental platforms where multipartite entanglement is inherently present. High-dimensional quantum systems provide an attractive route for investigating these resources while simultaneously reducing hardware overhead for quantum information processing. Here we realize a programmable four-dimensional optical qudit encoded in a single trapped $^{138}\mathrm{Ba}^{+}$ ion and demonstrate universal coherent control through phase-programmable optical rotations. Using this platform, we implement an entanglement-free realization of Grover's quantum search algorithm, achieving target-state identification probabilities of up to $94.5\pm2.0\%$. Within the same processor, we further demonstrate state-dependent quantum contextuality through a Clauser--Horne--Shimony--Holt (CHSH)-type noncontextuality inequality, obtaining a maximum violation of $S = 2.816 \pm 0.082$, in close agreement with the Tsirelson bound. By integrating programmable quantum computation and contextuality measurements within a single multilevel trapped-ion platform, our work establishes a versatile architecture for investigating the relationship between coherent interference and contextuality in quantum information processing and provides a scalable route toward high-dimensional quantum technologies.

Quantum computers can provide solutions to classically intractable problems under specific and adequate conditions. However, current devices have only limited computational resources, and an effort is made to develop useful quantum algorithms under these circumstances. This work experimentally demonstrates that a single-qubit device can host a universal classifier. The quantum processor used in this work is based on ion traps, providing highly accurate control on small systems. The algorithm chosen is the re-uploading scheme, which can address general learning tasks. Ion traps suit the needs of accurate control required by re-uploading. In the experiment here presented, a set of non-trivial classification tasks are successfully carried. The training procedure is performed in two steps combining simulation and experiment. Final results are benchmarked against exact simulations of the same method and also classical algorithms, showing a competitive performance of the ion-trap quantum classifier. This work constitutes the first experimental implementation of a classification algorithm based on the re-uploading scheme.