Related papers: Quantum Random Walks and Time Reversal
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…
Functors from (co)operads to bialgebras relate Hopf algebras that occur in renormalisation to operads, which simplifies the proof of the Hopf algebra axioms, and induces a characterisation of the corresponding group of characters and Lie…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
Statistical physics is important in understanding the physics of interacting many bodies. This has been historically developed by attempts to understand colliding gases and quantifying quantities like entropy, free energy, and other…
We establish a novel type of connection between random walks and analytic number theory. Working with a random walk on the circle group $\mathbb{R}/\mathbb{Z}$ in which each step is a random integer multiple of a given quadratic irrational…
The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…
We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras.
We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schr\"odinger-Heisenberg…
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…
Using the standard formulation of algebraic random walks (ARWs) via coalgebras, we consider ARWs for co-and Hopf-algebraic structures in the ring of symmetric functions. These derive from different types of products by dualisation, giving…
Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $\kappa$-Poincar\'e $T$-matrix is explicitly worked out.…
By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a 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…
Here we extend the algebro-geometric approach to free probability, started in~\cite{FMcK4,F14}, to general (non)-commutative probability theories. We show that any universal convolution product of moments of independent (non)-commutative…
In this paper we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e. the limit state if…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…