Efficient quantum algorithm to construct arbitrary Dicke states
arXiv:1209.5932
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).
After posting this draft to the arxiv (September 26, 2012), we received an email from Prof. Andrew M. Childs on October 3, 2012, referring [2] that also considered the same problem. However, our work is independent and uses a different approach. We were not aware of [2] while posting this draft for the first time. We have now included additional material and a detailed comparison with [2]
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