Related papers: Diagrammatic Approach to Quantum Search
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that for a set of optimal quantum walk times and marked…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with…
Graph representations are a powerful concept for solving complex problems across natural science, as patterns of connectivity can give rise to a multitude of emergent phenomena. Graph-based approaches have proven particularly fruitful in…
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…
The staggered quantum walk model allows to establish an unprecedented connection between discrete-time quantum walks and graph theory. We call attention to the fact that a large subclass of the coined model is included in Szegedy's model,…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put. They have been used to speed up spatial search on a variety of graphs,…
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…