Related papers: Quantum walk on simplicial complexes for simplicia…
We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are…
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…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…
Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
This work introduces a graph-phased Szegedy's quantum walk, which incorporates link phases and local arbitrary phase rotations (APR), unlocking new possibilities for quantum algorithm efficiency. We demonstrate how to adapt quantum circuits…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
In this work, we introduce a general form of a two-parameter family of local interactions between quantum walkers conditioned on the internal state of their coins. By choosing their particular case, we systematically study the impact of…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…
Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal quantum gate set. In this paper, we examine computation by quantum walks in terms of language…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…
We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the…
A quantum walk on a toral phase space involving translations in position and its conjugate momentum is studied in the simple context of a coined walker in discrete time. The resultant walk, with a family of coins parametrized by an angle is…