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Simulation of Quantum Walks using HPC

doi: 10.6062/jcis.2015.06.01.0092

(Free PDF)

Authors

Pedro C. S. Lara, Aaron Leão, Renato Portugal

Abstract

We describe program Hiperwalk, which is a new simulator of the main quantum walk models using high-performance computing (HPC). The simulator is able to generate the dynamics of discrete-time quantum walks and staggered quantum walks, and will be able simulate continuous-time quantum walks and Szegedy's quantum walks. It has an user-friendly input and is able to use hybrid HPC architectures, which includes the main ones available nowadays. The simulator outputs the main statistics associated with the probability distribution of the quantum walk in data files and automatically generates plots. The simulator uses open-source non-proprietary codes and employs freeware languages: Python, Neblina, Gnuplot, and OpenCL.

Keywords

quantum walks, HPC, simulation, parallel programming languages, quantum computing, quantum algorithms.

References

[1] G. Abal, R. Donangelo, M. Forets, and R. Portugal. Spatial quantum search in a triangular network. Mathematical Structures in Computer Science, 22:1-11, 2012.

[2] G. Abal, R. Donangelo, F. L. Marquezino, and R. Portugal. Spatial search on a honeycomb network. Mathematical Structures in Computer Science, 20:999-1009, 2010.

[3] D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani. Quantum walks on graphs. In Proceedings of the 33rd ACM Symposium on Theory of computing, pages 50-59, 2000. arXiv:quant-ph/0012090.

[4] Y. Aharonov, L. Davidovich, and N. Zagury. Quantum random walks. Physical Review A, 48(2):1687-1690, 1993.

[5] D. Aldous and J. Fill. Reversible Markov Chains and Random Walks on Graphs. Monography in preparation, 1994. http://www.stat.berkeley.edu/\textasciitildealdous/RWG/book.html.

[6] A. Ambainis, A. Backurs, N. Nahimov, R. Ozols, and A. Rivosh. Search by quantum walks on twodimensional grids without amplitude amplification. arvix:quant-ph/1112.3337, 2011.

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