d-pod realization of nonadiabatic holonomic quantum computation
Abstract
Holonomic quantum computation (HQC) realizes quantum gates through non-Abelian geometric phases, providing an experimentally accessible approach to quantum control. While the nonadiabatic HQC framework has been extensively developed for three-level Λ systems encoding qubits, its systematic extension to higher-dimensional qudits remains largely unexplored. In this work, we generalize nonadiabatic HQC to a d-pod configuration, where a single excited state is coupled to d ground states, the latter forming the computational subspace. This scheme enables universal holonomic single- and two-qudit gates using only optical or microwave pulses on trapped atoms or ions, offering an efficient route to implement a discrete universal gate set with minimal pulse coordination. As an explicit example, we analyze in detail the qutrit (d=3) case, demonstrating compact realizations of single- and two-qutrit holonomic gates, each gate requiring at most two loops in the Grassmannian generated by at most three pulses.
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BibTeX
@misc{axelsson2026dpod,
title = {{$d$-pod realization of nonadiabatic holonomic quantum computation}},
author = {Oskar Axelsson and Claes Fälth and Elias Henriksson Lindberg and Erik Sjöqvist},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16216},
eprint = {2609.16216},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16216},
}
RIS
TY - UNPB
TI - d-pod realization of nonadiabatic holonomic quantum computation
AU - Oskar Axelsson
AU - Claes Fälth
AU - Elias Henriksson Lindberg
AU - Erik Sjöqvist
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.16216
UR - https://arxiv.org/abs/2609.16216
AB - Holonomic quantum computation (HQC) realizes quantum gates through non-Abelian geometric phases, providing an experimentally accessible approach to quantum control. While the nonadiabatic HQC framework has been extensively developed for three-level Λ systems encoding qubits, its systematic extension to higher-dimensional qudits remains largely unexplored. In this work, we generalize nonadiabatic HQC to a d-pod configuration, where a single excited state is coupled to d ground states, the latter forming the computational subspace. This scheme enables universal holonomic single- and two-qudit gates using only optical or microwave pulses on trapped atoms or ions, offering an efficient route to implement a discrete universal gate set with minimal pulse coordination. As an explicit example, we analyze in detail the qutrit (d=3) case, demonstrating compact realizations of single- and two-qutrit holonomic gates, each gate requiring at most two loops in the Grassmannian generated by at most three pulses.
ER -