Searching via Nonlinear Quantum Walk on the 2D-Grid
Abstract
:1. Introduction
2. Model
2.1. The Linear Algorithm
Algorithm 1: Searching algorithm for the -grid |
2.2. Adding a Nonlinearity
Algorithm 2: Searching with a nonlinear algorithm for the -grid |
3. Numerical Results
4. Scale Analysis
- A strictly linear regime, when , which appears periodically with a period
- A nonlinear regime, when is maximum. In this case, and consequently the period is constant:
5. Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Di Molfetta, G.; Herzog, B. Searching via Nonlinear Quantum Walk on the 2D-Grid. Algorithms 2020, 13, 305. https://doi.org/10.3390/a13110305
Di Molfetta G, Herzog B. Searching via Nonlinear Quantum Walk on the 2D-Grid. Algorithms. 2020; 13(11):305. https://doi.org/10.3390/a13110305
Chicago/Turabian StyleDi Molfetta, Giuseppe, and Basile Herzog. 2020. "Searching via Nonlinear Quantum Walk on the 2D-Grid" Algorithms 13, no. 11: 305. https://doi.org/10.3390/a13110305