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Quantum Information Processing

Phase transition of a continuous-time quantum walk on the half line

  • 01-07-2024
Published in:
Author
Takuya Machida
Published in
Quantum Information Processing | Issue 7/2024

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Abstract

The article investigates the long-time behavior of a continuous-time quantum walk on the half line, defined by a spatially 2-periodic Hamiltonian. Unlike previous studies on quantum walks, this research employs Laplace transform to derive a limit theorem, revealing a phase transition between localization and delocalization of quantum walkers. The study highlights the challenges and differences in analyzing quantum walks at the edge of a half line compared to other locations. The main result is a limit theorem that describes the finding probability of the walker, with numerical experiments and discussions on invariant states providing additional insights. This work contributes to the understanding of quantum walks and their asymptotic behavior, offering a foundation for further research in quantum computing and simulations.
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next article Cryptographic enhancement of image data security through quantum-classical hybrid encryption with parameterized pixel ratios
Title
Phase transition of a continuous-time quantum walk on the half line
Author
Takuya Machida
Publication date
01-07-2024
Publisher
Springer US
Published in
Quantum Information Processing / Issue 7/2024
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-024-04455-1
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