Adding self-loops at each vertex of a graph improves the performance of quantum walks algorithms over loopless algorithms. Many works approach quantum walks to search for a single marked vertex. In this article, we experimentally address several problems related to quantum walk in the hypercube with self-loops to search for multiple marked vertices. We first investigate the quantum walk in the loopless hypercube. We saw that neighbor vertices are also amplified and that approximately $1/2$ of the system energy is concentrated in them. We show that the optimal value of $l$ for a single marked vertex is not optimal for multiple marked vertices. We define a new value of $l = (n/N)\cdot k$ to search multiple marked vertices. Next, we use this new value of $l$ found to analyze the search for multiple marked vertices non-adjacent and show that the probability of success is close to $1$. We also use the new value of $l$ found to analyze the search for several marked vertices that are adjacent and show that the probability of success is directly proportional to the density of marked vertices in the neighborhood. We also show that, in the case where neighbors are marked, if there is at least one non-adjacent marked vertex, the probability of success increases to close to $1$. The results found show that the self-loop value for the quantum walk in the hypercube to search for several marked vertices is $l = (n / N) \cdot k $.

Lackadaisical quantum walk in the hypercube to search for multiple marked vertices

**Chairs:** Gina Oliveira, Karina Valdivia and Andre Britto

Metaheuristics and Optimization II

technical paper

**BRACIS** originated from the combination of the two most important scientific events in Brazil in Artificial Intelligence (AI) and Computational Intelligence (CI): the Brazilian Symposium on Artificial Intelligence – **SBIA** (22 editions), and the Brazilian Symposium on Neural Networks – **SBRN** (13 editions). **ENIAC** is a national forum for researchers, practitioners, educators and students to present and discuss innovations, trends, experiences, developments and work in progress in the fields of Artificial and Computational Intelligence. **STIL** is the bi-annual Language Technology event.
All events are supported by the Brazilian Computer Society – Special Interest Groups: **CE-IA**, **CE-IC** and **CE-PLN**.

To access the 10th Brazilian Conference on Intelligent Systems (**BRACIS**), you need to register for the conference.  Please visit the Conference official site to register

[Register now](http://c4ai.inova.usp.br/bracis2021/)

Register now

BRACIS 2021

BRACIS originated from the combination of the two most important scientific events in Brazil in Artificial Intelligence (AI) and Computational Intelligence (CI): the Brazilian Symposium on Artificial Intelligence – SBIA (22 editions), and the Brazilian Symposium on Neural Networks – SBRN (13 editions). 
ENIAC is a national forum for researchers, practitioners, educators and students to present and discuss innovations, trends, experiences, developments and work in progress in the fields of Artificial and Computational Intelligence. 
STIL is the bi-annual Language Technology event.
All events are supported by the Brazilian Computer Society – Special Interest Groups: CE-IA, CE-IC and CE-PLN

Jonathan H. A. de Carvalho

1

1

Presentations

Lackadaisical quantum walk in the hypercube to search for multiple marked vertices

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES