Related papers: The discrete-time quaternionic quantum walk on a g…
The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
This study is motivated by the previous work [14]. We treat 3 types of the one-dimensional quantum walks (QWs), whose time evolutions are described by diagonal unitary matrix, and diagonal unitary matrices with one defect. In this paper, we…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
The poses of $m$ robotics in $n$ time points may be represented by an $m \times n$ dual quaternion matrix. In this paper, we study the spectral theory of dual quaternion matrices. We introduce right and left eigenvalues for square dual…
The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of…
We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs) for combinatorial optimisation with mixing unitaries defined by vertex-transitive graphs, based on their continuous-time…
A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
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…
We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum…
The most elementary quantum walk is characterized by a 2-dimensional unitary coin flip matrix, which can be parameterized by 4 real variables. The influence of the choice of the coin flip matrix on the time evolution operator is analysed in…
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…
The time evolutions of discrete-time quantum walks on graphs are determined by the local adjacency relations of the graphs. In this paper, first, we construct a discrete-time quantum walk model that reflects the embedding on the surface so…
The interest in quantum walks has been steadily increasing during the last two decades. It is still worth to present new forms of quantum walks that might find practical applications and new physical behaviors. In this work, we define…
This paper is motivated by the following problem. Define a quantum walk on a positively weighted path (linear chain). Can the weights be tuned so that perfect state transfer occurs between the first vertex and any other position? We do not…
In this paper, we determine periodicity of quantum walks defined by mixed paths and mixed cycles. By the spectral mapping theorem of quantum walks, consideration of periodicity is reduced to eigenvalue analysis of $\eta$-Hermitian adjacency…