相关论文: Quantum random walks and their convergence
The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect…
A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…
It is shown how to construct quantum random walks with particles in an arbitrary faithful normal state. A convergence theorem is obtained for such walks, which demonstrates a thermalisation effect: the limit cocycle obeys a quantum…
Quantum random walks, - coined, lattice ones, - exhibit ballistic behavior with fascinating asymptotic patterns of the amplitudes. We show that averaging over the coins (using the Haar measure), these patterns blend into a spline. Also, we…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
We propose an experimental realization of discrete quantum random walks using neutral atoms trapped in optical lattices. The random walk is taking place in position space and experimental implementation with present day technology --even…
We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple…