Disorder And Decoherence In Quantum Walks

Since the concept of quantum walk was proposed in 1993,quantum walk as a phys-ical process has received a lot of research in the fields of physics and computer science,and quantum walk is widely used in quantum information theory.In recent years,our country attaches great importance to the development of the quantum field.Therefor,it is meaningful to use mathematical viewpoints to study quantum walk.This article aims to use mathematical modeling methods to study quantum walk in open systems,and the main work is as follows:(1)We introduce the concept of diamond product,and a quantum walk model with environment is proposed.More specifically,we take the coin operator on C~2and the square integrable Bernoulli functional space h on the unitary operator representing the environment as the diamond product.Then we prove that these diamond products are still coin operators on h,so we can use them to define a quantum walk model with environ-ment,In physics,we can interpret this model as the quantum walk is randomly disordered by the environment.(2)We use Fourier transform to investigate the construction properties of the quan-tum walk model with environment and the representation of the model in the functional space framework is given.The decoherence of quantum walk based on quantum Bernoulli noise is analyzed,and we prove that in some special initial states,quantum walk based on quantum Bernoulli noise can be degenerated into Classic Markov chain.In addition,this article also discussed other related issues,and we also got the corre-sponding results.