Efficient quantum algorithm to construct arbitrary Dicke states

TL;DR

This paper presents an efficient quantum algorithm for constructing any arbitrary Dicke state by integrating symmetric Boolean functions, Krawtchouk polynomials, and quantum algorithms like Deutsch-Jozsa and Grover, with potential improvements from biased Hadamard transformations.

Contribution

It introduces a novel quantum algorithm that combines multiple quantum techniques and mathematical tools for efficient Dicke state construction, extending previous methods.

Findings

Algorithm efficiently constructs arbitrary Dicke states.

Integration of Krawtchouk polynomials enhances state manipulation.

Comparison shows improvements over previous approaches.

Abstract

In this paper, we study efficient algorithms towards the construction of any arbitrary Dicke state. Our contribution is to use proper symmetric Boolean functions that involve manipulations with Krawtchouk polynomials. Deutsch-Jozsa algorithm, Grover algorithm and the parity measurement technique are stitched together to devise the complete algorithm. Further, motivated by the work of Childs et al (2002), we explore how one can plug the biased Hadamard transformation in our strategy. Our work compares fairly with the results of Childs et al (2002).