相关论文: Quantum walks as a probe of structural anomalies i…

Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…

Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…

The exponential speed-up of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that…

It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…

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…

Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…

Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…

Quantum walks with memory(QWM) are a type of modified quantum walks that record the walker's latest path. As we know, only two kinds of QWM are presented up to now. It is desired to design more QWM for research, so that we can explore the…

Recently, the work on quantum automorphism groups of graphs has seen renewed progress, which we expand in this paper. Quantum symmetry is a richer notion of symmetry than the classical symmetries of a graph. In general, it is non-trivial to…

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…

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…

A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…

We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…

In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

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…

Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…

In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to…

We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…