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- Franklin L. Marquezino, Renato Portugal
- Computer Physics Communications
- 2008

Several research groups are giving special attention to quantum walks recently, because this research area have been used with success in the development of new efficient quantum algorithms. A general simulator of quantum walks is very important for the development of this area, since it allows the researchers to focus on the mathematical and physical… (More)

- F. L. Marquezino
- 2008

The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean probability distribution of a discrete-time quantum walk on a hypercube mixes to a (generally non-uniform) distribution π(x) in… (More)

- Gonzalo Abal, Raul Donangelo, Franklin L. Marquezino, Renato Portugal
- Mathematical Structures in Computer Science
- 2010

The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. We propose a quantum algorithm for the spatial search problem on a honeycomb lattice with N sites and torus-like boundary conditions. The search… (More)

- Franklin L. Marquezino, Renato Portugal, Gonzalo Abal
- ArXiv
- 2010

Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving… (More)

—We propose the theory of Cayley graphs as a framework to analyse gate counts and quantum costs resulting from reversible circuit synthesis. Several methods have been proposed in the reversible logic synthesis literature by considering different libraries whose gates are associated to the generating sets of certain Cayley graphs. In a Cayley graph, the… (More)

- F L Marquezino, R R Mello Júnior
- 2004

This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, beginning by the concept of bit and its representation with classical physical systems, and then going to the concept of quantum bit (the so-called " qubit ") and exposing some differences and similarities.This paper is intended… (More)

- S. A. Grillo, Franklin L. Marquezino
- ArXiv
- 2016

In theoretical quantum computer science, understanding where and how computational speed-ups occur while applying quantum properties is a primary goal. In this paper, we study such problem under the framework of Quantum Query Model and prove the significance of L1-norm in the simulation of a given quantum algorithm. This result is presented by upper-bounds… (More)

- S. A. Grillo, Franklin L. Marquezino
- ArXiv
- 2016

The Quantum Query Model is a framework that allow us to express most known quantum algorithms. Algorithms represented by this model consist on a set of unitary operators acting over a finite Hilbert space, and a final measurement step consisting on a set of projectors. In this work, we prove that the application of these unitary operators before the… (More)