Limit theorems and absorption problems for quantum random walks in one dimension
نویسنده
چکیده
In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by 2 × 2 unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.
منابع مشابه
Limit Theorems and Absorption Probrems for Quantum Random Walks in One Dimension
In this paper we review our recent results on limit theorems and absorption problems for the one-dimensional quantum random walk determined by 2× 2 unitary matrix.
متن کاملLimit theorems and absorption problems for one-dimensional correlated random walks
There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between both walks and study limit theorems and absorption problems for correlated random walks by our PQRS method, which was used in our analysis of quantum walks.
متن کاملOne-dimensional discrete-time quantum walks on random environments
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.
متن کاملAbsorption Problems for Quantum Random Walks in One Dimension
This paper treats absorption problems for the one-dimensional quantum random walk determined by a 2× 2 unitary matrix U on a state space {0, 1, . . . ,N} where N is finite or infinite by using a new path integral approach based on an orthonormal basis P,Q,R and S of the vector space of complex 2× 2 matrices. Our method studied here is a natural extension of the approach in the classical random ...
متن کاملDynamic Quantum Bernoulli Random Walks
Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviations principl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Quantum Information & Computation
دوره 2 شماره
صفحات -
تاریخ انتشار 2002