Related papers: Quantum Severalty: Speed-up and Suppress Effect in…
Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it…
Continuous-time quantum walks are typically effected by either the discrete Laplacian or the adjacency matrix. In this paper, we explore a third option: the signless Laplacian, which has applications in algebraic graph theory and may arise…
A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial…
Continuous-time quantum walks provide an alternative method for quantum search problems. Most of the earlier studies confirmed that quadratic speedup exists in some synthetic Hamiltonians, but whether there is quadratic speedup in real…
Traditional tree search algorithms supply a blueprint for modeling problem solving behaviour. A diverse spectrum of problems can be formulated in terms of tree search. Quantum computation, in particular Grover's algorithm, has aroused a…
Grover's search algorithm was a groundbreaking advancement in quantum algorithms, displaying a quadratic speed-up of querying for items. Since the creation of this algorithm it has been utilized in various ways, including in preparing…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
Quantum walks are powerful tools for building quantum search algorithms or quantum sampling algorithms named the construction of quantum stationary state. However, the success probability of those algorithms are all far away from 1.…
Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Quantum walks provide a powerful framework for achieving algorithmic speedup in quantum computing. This paper presents a quantum search algorithm for 2-tessellable graphs, a generalization of bipartite graphs, achieving a quadratic speedup…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
The Travelling Salesman Problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we…
In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of $O(1/\log N)$ in $O(\sqrt{N \log N})$ steps, which with amplitude amplification yields an overall runtime…