Related papers: Two-particle quantum walks applied to the graph is…
We investigate the quantum dynamics of particles on graphs ("quantum random walks"), with the aim of developing quantum algorithms for determining if two graphs are isomorphic (related to each other by a relabeling of vertices). We focus on…
Berry and Wang [Phys. Rev. A {\bf 83}, 042317 (2011)] show numerically that a discrete-time quantum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we…
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…
We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous time quantum walks in a one-dimensional ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is…
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…
We investigate continuous-time quantum walks of two indistinguishable particles [bosons, fermions or hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are well consistent with…
We investigate the graph isomorphism (GI) in some cospectral networks. Two graph are isomorphic when they are related to each other by a relabeling of the graph vertices. We want to investigate the GI in two scalable (n + 2)-regular graphs…
This paper explores the entanglement dynamics generated by interacting two-particle quantum walks on degree-regular and -irregular graphs. We performed spectral analysis of the time-evolution of both the particle probability distribution…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…
We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Up to now the experimental…
Asymptotic dynamics of a Hadamard walk of two non-interacting quantum particles on a dynamically percolated finite line or a circle is investigated. We construct a basis of the attractor space of the corresponding random-unitary dynamics…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
Quantum particles are known to be faster than classical when they propagate stochastically on certain graphs. A time needed for a particle to reach a target node on a distance, the hitting time, can be exponentially less for quantum walks…
Quantum walks of interacting particles may display non-trivial features due to the interplay between the statistical nature and the many-body interactions associated to them. We analyze the quantum walk of interacting defects on top of an…
Progress in the reliable preparation, coherent propagation and efficient detection of many-body states has recently brought collective quantum phenomena of many identical particles into the spotlight. This tutorial introduces the physics of…
The article deals with one- and two-particle quantum walks on a graph with Braess-like topology and analyzes the issue of network congestion in the quantum world. Our approach to the study of congestion in quantum networks is based on the…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…