Analysis of the action of conventional trapped-ion entangling gates in qudit space

TL;DR

This paper investigates the phase complexities in trapped-ion qudit gates, proposing compensation methods to improve gate robustness and facilitate scalable qudit quantum computing.

Contribution

It introduces theoretical analysis and practical methods for phase compensation in multi-level trapped-ion gates, advancing qudit quantum processor development.

Findings

Identified phase accumulation issues in Mølmer–Sørensen and Light-shift gates.

Developed active compensation techniques for phase errors.

Enhanced gate robustness and simplified native gate structures.

Abstract

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 entangling and non-entangling phases, accumulated in M\o lmer--S\o rensen 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.