相关论文: Relation between coined quantum walks and quantum …

Quantum walk is a synonym for multi-path interference and faster spread of a particle in a superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational…

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…

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…

Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is…

A method of quantization of classical soliton cellular automata (QSCA) is put forward that provides a description of their time evolution operator by means of quantum circuits that involve quantum gates from which the associated Hamiltonian…

The continuous limit of quantum walks (QWs) on the line is revisited through a recently developed method. In all cases but one, the limit coincides with the dynamics of a Dirac fermion coupled to an artificial electric and/or relativistic…

We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time…

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 cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum…

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…

Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the…

We give a characterization of the line digraph of a regular digraph. We make use of the characterization, to show that the underlying digraph of a coined quantum random walk is a line digraph. We remark the connection between line digraphs…

Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial…

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…

Quantum devices featuring mid-circuit measurement and reset capabilities, such as quantum computers and dual-species Rydberg quantum simulators, enable the realization of quantum cellular automata. These systems evolve in discrete time…

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…

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

Quantum Random Walks, which have drawn much attention over the past few decades for their distinctly non-classical behavior, is a promising subfield within Quantum Computing. Theoretical framework and applications for these walks have seen…