Related papers: Properties of Open Quantum Walks on $\mathbb{Z}$
We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic…
We devise a protocol to build 1D time-dependent quantum walks in 1D maximizing the spatial spread throughout the procedure. We allow only one of the physical parameters of the coin-tossing operator to vary, i.e. the angle $\theta$, such…
The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…
Quantum walks with long-range steps $R^{-\gamma}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma\geq2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a…
We consider a quantum particle (walker) on a line who coherently chooses to jump to the left or right depending on the result of toss of a quantum coin. The lengths of the jumps are considered to be independent and identically distributed…
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…
We consider the Grover walk on a finite graph composed of two arbitrary simple graphs connected by one edge, referred to as a bridge. The parameter $\epsilon>0$ assigned at the bridge represents the strength of connectivity: if…
We introduce the concept of a quantum walk with two particles and study it for the case of a discrete time walk on a line. A quantum walk with more than one particle may contain entanglement, thus offering a resource unavailable in the…
The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic…
An open quantum walk formalism for dissipative quantum computing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on…
The dynamics of a one dimensional quantum walker on the lattice with two internal degrees of freedom, the coin states, is considered. The discrete time unitary dynamics is determined by the repeated action of a coin operator in U(2) on the…
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…
In the present paper, we construct QMCs associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution…
The analysis of logarithmic return distributions defined over large time scales is crucial for understanding the long-term dynamics of asset price movements. For large time scales of the order of two trading years, the anticipated Gaussian…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
Properties of the probability distribution generated by a discrete-time quantum walk, such as the number of peaks it contains, depend strongly on the choice of the initial condition. In the present paper we discuss from this point of view…
Quantum walks are more than tools for building quantum algorithms. They have been used effectively to model and simulate quantum dynamics in many complex physical processes. Particularly, a variant of discrete-time quantum walk known as…
We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than…
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…