Coined quantum walks on percolation graphs

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line) we introduce a simple notion of quantum tunneling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero, as the percolation probability decreases to the critical point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after referee comments, added extra figur

Asymptotic entanglement in a two-dimensional quantum walk

The evolution operator of a discrete-time quantum walk involves a conditional shift in position space which entangles the coin and position degrees of freedom of the walker. After several steps, the coin-position entanglement (CPE) converges to a well defined value which depends on the initial state. In this work we provide an analytical method which allows for the exact calculation of the asymptotic reduced density operator and the corresponding CPE for a discrete-time quantum walk on a two-dimensional lattice. We use the von Neumann entropy of the reduced density operator as an entanglement measure. The method is applied to the case of a Hadamard walk for which the dependence of the resulting CPE on initial conditions is obtained. Initial states leading to maximum or minimum CPE are identified and the relation between the coin or position entanglement present in the initial state of the walker and the final level of CPE is discussed. The CPE obtained from separable initial states satisfies an additivity property in terms of CPE of the corresponding one-dimensional cases. Non-local initial conditions are also considered and we find that the extreme case of an initial uniform position distribution leads to the largest CPE variation.Comment: Major revision. Improved structure. Theoretical results are now separated from specific examples. Most figures have been replaced by new versions. The paper is now significantly reduced in size: 11 pages, 7 figure

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

Chemical weed management programs for cycloxydim-tolerant maize in Iran

In order to introduce new chemical weed management program in maize weed control in Iran, a study was conducted during 2014 and 2015. Experiment were carried out in a randomized complete block design with three replications. 15 treatments of the common maize herbicides, including nicosulfuron, foramsulforon, eradicane and 2,4-D + MCPA were applied in their recommended doses, moreover the treatments related to cycloxydim with dicamba + tritosulfuron were used with different doses and in different times along with two control treatments (weedy and weed-free). Treatments contained 75-150 g a.i. ha-1 of cycloxydim, showed similar results with the common treatments including nicosulfuron, foramsulforon, eradicane and 2,4-D + MCPA. However, treatments with high doses of cycloxydim, had a significant reduction in weed density and weed biomass. There were no significant differences between the effects of treatments on maize grain yield and biomass. Despite the acceptable weed control of the combined treatment of cycloxydim with dicamba plus tritosulfuron, maize canopy could overcome weed growth. Based on the results and by considering cycloxydim efficacy in controlling perennial grassy weeds in maize plantation, this chemical is a suitable option during different growing stages of weeds and maize. Finally, the application of 200-300 g a.i. ha-1 of cycloxydim combined with dicamba plus tritosulfuron was the best option from an economic and environmental safety points of view. © 2020, Tarbiat Modares University. All rights reserved