# One-dimensional quantum walk with a moving boundary

## Abstract

Quantum walks are interesting models with potential applications to quantum algorithms and physical processes such as photosynthesis. In this paper, we study two models of one-dimensional quantum walks, namely, quantum walks with a moving absorbing wall and quantum walks with one stationary and one moving absorbing wall. For the former, we calculate numerically the survival probability, the rate of change of average position, and the rate of change of standard deviation of the particle's position in the long time limit for different wall velocities. Moreover, we also study the asymptotic behavior and the dependence of the survival probability on the initial particle's state. While for the latter, we compute the absorption probability of the right stationary wall for different velocities and initial positions of the left wall boundary. The results for these two models are compared with those obtained for the classical model. The difference between the results obtained for the quantum and classical models can be attributed to the difference in the probability distributions.

- Authors:

- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)
- (Singapore)
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)

- Publication Date:

- OSTI Identifier:
- 22068664

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ABSORPTION; ALGORITHMS; ASYMPTOTIC SOLUTIONS; DISTRIBUTION; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; PROBABILITY; QUANTUM MECHANICS; VELOCITY

### Citation Formats

```
Kwek, Leong Chuan, National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, and Setiawan.
```*One-dimensional quantum walk with a moving boundary*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.032319.

```
Kwek, Leong Chuan, National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, & Setiawan.
```*One-dimensional quantum walk with a moving boundary*. United States. doi:10.1103/PHYSREVA.84.032319.

```
Kwek, Leong Chuan, National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, and Setiawan. Thu .
"One-dimensional quantum walk with a moving boundary". United States. doi:10.1103/PHYSREVA.84.032319.
```

```
@article{osti_22068664,
```

title = {One-dimensional quantum walk with a moving boundary},

author = {Kwek, Leong Chuan and National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616 and Setiawan},

abstractNote = {Quantum walks are interesting models with potential applications to quantum algorithms and physical processes such as photosynthesis. In this paper, we study two models of one-dimensional quantum walks, namely, quantum walks with a moving absorbing wall and quantum walks with one stationary and one moving absorbing wall. For the former, we calculate numerically the survival probability, the rate of change of average position, and the rate of change of standard deviation of the particle's position in the long time limit for different wall velocities. Moreover, we also study the asymptotic behavior and the dependence of the survival probability on the initial particle's state. While for the latter, we compute the absorption probability of the right stationary wall for different velocities and initial positions of the left wall boundary. The results for these two models are compared with those obtained for the classical model. The difference between the results obtained for the quantum and classical models can be attributed to the difference in the probability distributions.},

doi = {10.1103/PHYSREVA.84.032319},

journal = {Physical Review. A},

issn = {1050-2947},

number = 3,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}