Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Associations between Microbiological and Salivary Caries Activity Tests and Caries Experience in Hungarian Adolescents

The aim of the study was to assess caries prevalence in connection with salivary caries-related findings in 349 14- to 16-year-old Hungarian adolescents living in two different cities. DMFT, DMFS means, stimulated salivary flow, buffer capacity, mutans streptococci, lactobacilli and candida counts in saliva were determined. The ratio of caries-free adolescents was 4.6% in the total population sample, DMFT mean values were 7.24B4.86, DMFS means 10.50B8.35. Mean secretion rate of stimulated saliva was 0.84B0.50; a low buffer capacity was found in 6.3% of the examined children. The ratio of carriers of mutans streptococci, lactobacilli and yeasts in saliva was 89.7, 73.9 and 47.7%, respectively. DMFT and DMFS values as well as mutans streptococci and candida counts were lower in the capital than in the other city. Statistically significant correlations were found between DMFT, DMFS mean values, and salivary microbiological counts

Simulations of two-particle interactions with 2D quantum walks in time

© 2014 AIP Publishing LLC. We present the experimental implementation of a quantum walk on a two-dimensional lattice and show how to employ the optical system to simulate the quantum propagation of two interacting particles. Our quantum walk in time transfers the spatial spread of a quantum walk into the time domain, which guarantees a high stability and scalability of the setup. We present with our device quantum walks over 12 steps on a 2D lattice. By changing the properties of the driving quantum coin, we investigate different kinds of two-particle interactions and reveal their impact on the occurring quantum propagation

Quantum simulations with a two-dimensional quantum walk

We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states. © 2012 OSA

Photons walking the line:A quantum walk with adjustable coin operations

We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker’s position Hilbert space is increased. We observed a non-Gaussian distribution of the walker’s final position, thus characterizing a faster spread of the photon wave packet in comparison to the classical random walk. The walk is realized for many different coin settings and initial states, opening the way for the implementation of a quantum-walk-based search algorithm