arXiv subjects

Bhanu Pratap Yadav

Publications and source records attributed to Bhanu Pratap Yadav.

3 recordsLinked to original sources

arXiv2026

Bounds in the Projective Unitary Group with Respect to Global Phase Invariant Metric

We consider a global phase-invariant metric in the projective unitary group PUn, relevant for universal quantum computing. We obtain the volume and measure of small metric ball in PUn and derive the Gilbert-Varshamov and Hamming bounds in PUn. In addition, we provide upper and lower bounds for the kissing radius of the codebooks in PUn as a function of the minimum distance. Using the lower bound of the kissing radius, we find a tight Hamming bound. Also, we establish bounds on the distortion-rate function for quantizing a source uniformly distributed over PUn. As example codebooks in PUn, we consider the projective Pauli and Clifford groups, as well as the projective group of diagonal gates in the Clifford hierarchy, and find their minimum distances. For any code in PUn with given cardinality we provide a lower bound of covering radius. Also, we provide expected value of the covering radius of randomly distributed points on PUn, when cardinality of code is sufficiently large. We discuss codebooks at various stages of the projective Clifford + T and projective Clifford + S constructions in PU2, and obtain their minimum distance, distortion, and covering radius. Finally, we verify the analytical results by simulation.

quant-ph↗

arXiv2020

New Classes of Quantum Codes Associated with Surface Maps

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 $.

math.CO↗

arXiv2020

Semi-equivelar maps on the surface of Euler genus 3

If the cyclic sequence of faces for all the vertices in a map are of same type, then the map is said to be a semi-equivelar map. In this article, we classify all the types of semi-equivelar maps on the surface of Euler genus 3, $i.e.$, on the surface of Euler characteristic $-1$. That is, we present {a complete map types of} semi-equivelar maps (if exist) on the surface of Euler char. $-1$. We know the complete list of semi-equivelar maps (upto isomorphism) for some types. Here, we also present a complete list of semi-equivelar maps for one type and for other types, similar steps can be followed.

math.CO↗