Related papers: Two-particle quantum walks applied to the graph is…
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…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
We examine a system of interacting random walks with leftward drift on $\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of…
Graph Neural Networks (GNNs) have paved the way for being a cornerstone in graph-related learning tasks. Yet, the ability of GNNs to capture structural interactions within graphs remains under-explored. In this work, we address this gap by…
We study the quantum walks of two interacting spin-1 bosons. We derive an exact solution for the time-dependent wave function that describes the two-particle dynamics governed by the one-dimensional spin-1 Bose-Hubbard model. We show that…
We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a…
Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of…
In this work we propose a measure for the quantum discord of indistinguishable particles, based on the definition of entanglement of particles given in [H. M. Wiseman et al., Phis. Rev. Lett 91, 097902 (2003)]. This discord of particles is…
A quantum walk, \emph{i.e.}, the quantum evolution of a particle on a graph, is termed \emph{scalar} if the internal space of the moving particle (often called the coin) has a dimension one. Here, we study the existence of scalar quantum…
The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…
Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…
We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the…
Quantum graphs are defined by having a Laplacian defined on the edges of a metric graph with boundary conditions on each vertex such that the resulting operator, $\mathbf{L}$, is self-adjoint. We use Neumann boundary conditions although we…
I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and…
Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…