Coherence depletion in the Grover quantum search algorithm

By Hai-Long Shi, Siyuan Liu, Xiao-Hui Wang, Wen-Li Yang, Zhanying Yang, Heng Fan. 2016

149 citations recorded by the source corpus.

We investigate the role of quantum coherence depletion (QCD) in the Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure (${\mathcal{C}}_{r}$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the ${l}_{1}$ norm of coherence measure (${\mathcal{C}}_{{l}_{1}}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of the database, regardless of using ${\mathcal{C}}_{r}$ or ${\mathcal{C}}_{{l}_{1}}$. In the generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord, and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichny's inequality are not violated.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/ec332e1624e5b67d8b6d57ba400bd2df2b3143b8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

  1. Heng Fan
  2. Yi Peng
  3. Yu-Ran Zhang
  4. Jieci Wang
  5. Ming‐Liang Hu
  6. Xueyuan Hu

Citations in the corpus