Quantum maps

Debashis Bhowmik, Dipendu Maity, Bhanu Pratap Yadav +1 more

If the cyclic sequences of {face types} {at} all vertices in a map are the same, then the map is said to be a semi-equivelar map. In particular, a semi-equivelar map is equivelar if the faces are the same type. Homological quantum codes represent a subclass of topological quantum codes. In this article, we introduce {thirteen} new classes of quantum codes. These codes are associated with the following: (i) equivelar maps of type $ [k^k]$, (ii) equivelar maps on the double torus along with the covering of the maps, and (iii) semi-equivelar maps on the surface of \Echar{-1}, along with {their} covering maps. The encoding rate of the class of codes associated with the maps in (i) is such that $ \frac{k}{n}\rightarrow 1 $ as $ n\rightarrow\infty $, and for the remaining classes of codes, the encoding rate is $ \frac{k}{n}\rightarrow α$ as $ n\rightarrow \infty $ with $ α< 1 $.

H. H. Wills Physics Laboratory

Arul Murugan Lakshminarayanan

Constantino Rodriguez-Ramos, Colin Wilmott

Abstract In this paper, we consider the convex structure of the set of unital quantum channels. To do this, we introduce a novel framework to construct and characterise different families of low-rank unital quantum maps. In this framework, unital quantum maps are represented as a set of complex parameters on which we impose a set of constraints. The different families of unital maps are obtained by mapping those parameters into the operator representation of a quantum map. For these families, we also introduce a scalar measuring their distance to the set of mixed-unitary maps. We consider the particular case of qutrit channels which is the smallest set of maps for which the existence of non-unitary extremal maps is known. In this setting, we show how our framework generalises the description of well-known maps such as the antisymmetric Werner–Holevo map but also novel families of qutrit maps.

Jincheng Zhang

Quantum state mapping, a crucial technique in quantum information processing, involves the transformation of quantum states into different mappings. This research explores the interplay between these mappings and topological mappings, proposing a novel algorithm for optimizing quantum device control through this relationship. We introduce a framework based on non-linear mapping, aiming to precisely control quantum states by iteratively refining these mappings. The core mechanism centers on the identification of optimal mappings that leverage topological properties to enhance device performance. This work provides a new perspective on quantum device design, highlighting the potential of topological mappings to guide and improve the control of quantum systems. We demonstrate the effectiveness of this approach through simulations and preliminary device design, showcasing its ability to achieve targeted control and optimize device characteristics.

Claudio Conti