Related papers: Scaling Hypothesis of Spatial Search on Fractal La…
The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a vertex is marked only after reaching it. This problem is a…
Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice. We numerically study the quantum search algorithm based on the lackadaisical…
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk…
Continuous-time quantum walks (CTQW) have shown the capability to perform efficiently the spatial search of a marked site on many kinds of graphs. However, most of such graphs are hard to realize in an experimental setting. Here we study…
Iterative construction of a Sierpinski carpet or sponge is shown to be a critical phenomenon analogous to uncorrelated percolation. Critical exponents are derived or calculated (by random walks over the carpet or sponge at infinite…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice in the critical region are investigated. We study numerically two scaling functions:…
This comment is to correct the proof of optimality of quantum spatial search for Erd\H{o}s-R\'enyi graphs presented in `Spatial Search by Quantum Walk is Optimal for Almost all Graphs' (https://doi.org/10.1103/PhysRevLett.116.100501). The…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…
Spatial search is an important problem in quantum computation, which aims to find a marked vertex on a graph. We propose a novel approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum…
In view of promising applications of fractal nanostructures, we analyze the spectra of quantum particles in the Sierpinski carpet and study the non-correlated electron gas in this geometry. We show that the spectrum exhibits scale…
Orbital magnetization (OM) in Sierpinski carpet (SC) and triangle (ST) fractal is theoretically investigated by using Haldane model as a prototypical example. The OM calculation is performed following two distinct approaches; employing the…
We investigate asymptotical behavior of numbers of long Hamiltonian walks (HWs), i.e. self-avoiding random walks that visit every site of a lattice, on various fractal lattices. By applying an exact recursive technique we obtain scaling…
One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…
We study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space…
We study a random walk infiltration (RWI) model, in homogeneous and in fractal media, with localized sources at their boundaries. The particles released at a source, which is maintained at a constant density, execute unbiased random walks…
This paper deals with the problem of the requirements for quantum systems that enable one to design efficient quantum algorithms. We rise the issue of the possibility to utilise the non-complete networks for algorithmic purposes. In…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
We consider the discrete time quantum random walks on a Sierpinski gasket. We study the hitting probability as the level of fractal goes to infinity in terms of their localization exponents $\beta_w$ , total variation exponents $\delta_w$…
In this work, we consider the spatial search for a general marked state on graphs by continuous time quantum walks. As a simplest case, we compute the amplitude expression of the search for the multi-vertex uniform superposition state on…
A randomly walking quantum particle searches in Grover's $\Theta(\sqrt{N})$ iterations for a marked vertex on the complete graph of $N$ vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a…