Related papers: Classical approach to the graph isomorphism proble…
We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators,…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
We propose a novel method using a quantum annealer -- an analog quantum computer based on the principles of quantum adiabatic evolution -- to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are…
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time…
This article presents a new quantum PageRank algorithm on graphs using discrete-time open quantum walks. Google's PageRank is a widely used algorithm for ranking the web pages on the World Wide Web in classical computation. From a broader…
Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged…
We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence, and employ the quantum-classical (QC) dynamical distance as a figure of…
Currently there are three major paradigms of quantum computation, the gate model, annealing, and walks on graphs. The gate model and quantum walks on graphs are universal computation models, while annealing plays within a specific subset of…
The graph isomorphism problem remains a fundamental challenge in computer science, driving the search for efficient decision algorithms. Due to its ambiguous computational complexity, heuristic approaches such as simulated annealing are…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
We quantitatively differentiate between the spreads of discrete-time quantum and classical random walks on a cyclic graph. Due to the closed nature of any cyclic graph, there is additional "collision"- like interference in the quantum…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
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…
De novo DNA sequence assembly is based on finding paths in overlap graphs, which is a NP-hard problem. We developed a quantum algorithm for de novo assembly based on quantum walks in graphs. The overlap graph is partitioned repeatedly to…
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk…
Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
The classical random walk isomorphism theorems relate the local times of a continuous-time random walk to the square of a Gaussian free field. A Gaussian free field is a spin system that takes values in Euclidean space, and this article…
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 are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…