Topologically robust gates in holonomic quantum computation

According to the article published in Mod. Phys. Lett. A, Vol. 37, No. 27, 2250184 (2022), https://arxiv.org/abs/2202.01973
Holonomic quantum computation is a formulation of quantum computation where quantum gates are given by non-abelian geometric phases obtained from suitably chosen quantum evolutions. We show that for hamiltonians producing rotations, robust quantum gates can be built by using the topological properties of a particular class of antisymmetric quantum states, known as anticoherent planes, which generalize the anticoherent spin states, i.e., states whose polarization vector vanishes. In this seminar, after a short introduction to anticoherent spin states and the Majorana stellar representation, anticoherent planes and their geometric phases under rotations will be presented. We will explain how to generate noise-resistant quantum gates using this class of quantum states, and we will provide several illustrative examples. These results improve the already known robustness properties in holonomic quantum computation.