Higher dimensional entangled qudits in a trapped three-level ion

Rasim Dermez, S. Abdel‐Khalek, Kemal Kara +2 more

Mahmoud Abdel‐Aty, Arthur R. McGurn

Mahmoud Abdel‐Aty

Pavel Kamenskikh, Nikita Semenin, Ilia Zalivako +4 more

Qudits, or multi-level quantum information carriers, present a promising path for scaling quantum computers. However, their use introduces increased complexity in quantum logic, necessitating careful control of relative phases between different qudit levels. In trapped-ion systems, entangling operations accumulate phases on specific levels that are no longer global, unlike in qubit architectures. Furthermore, the structure of multi-level gates becomes increasingly intricate with higher-dimensional Hilbert spaces. This work explores the theory of these additional local and nonlocal phases, accumulated in Mølmer--Sørensen and Light-shift gates. We propose methods to actively compensate for these phases, enhance gate robustness against parameter fluctuations, and simplify native gates for more efficient circuit decomposition. Our results pave the way toward the practical and scalable implementation of qudit-based quantum processors.

Dietrich G. Leibfried

Rasim Dermez, Özgür Esat Müstecaplıoğlu

Higher dimensional quantum entanglement in a trapped three-level ion interacting with two laser beams in Λ scheme is investigated beyond the Lamb–Dicke limit. It is shown that higher dimensional entanglement can be established in a single step, with a tunable dimensionality and duration via the Lamb–Dicke parameter.