Related papers: A note on sequential walks
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…
This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.
We set the criteria under which superposition of causal order can be incorporated in to quantum walks. In particular, we show that only periodic quantum walks or those with at least one disorder exhibit Superposition of causal order under…
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…
We study a particular class of trace-preserving completely positive maps, called PQ-channels, for which classical and quantum evolutions are isolated in a certain sense. By combining open quantum random walks with a notion of recurrence, we…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We first present a comprehensive review of various random walk metrics used in the literature and express them in a consistent framework. We then introduce fundamental tensor -- a generalization of the well-known fundamental matrix -- and…
Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper marks the initial stride toward achieving this…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
The purpose of this short note is to establish a connection between a one-dimensional random walk in a random sparse environment and the random pinning model. We show that the grand canonical partition function of the pinning model…
We give a semantics to iterated update by a preference relation on possible developments. An iterated update is a sequence of formulas, giving (incomplete) information about successive states of the world. A development is a sequence of…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The…
We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which…
A new proof is given for the formula for the expected return time of a random walk on a graph. This proof makes use of known relationships between electric resistance and random walks.
We exhibit a one to one correspondence between some universal probabilistic properties of the ordering coordinate of one-dimensional Ising-like models and a class of continuous time random walks. This correspondence provides an new…
These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.