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Open Quantum Systems Decoherence
Quantum Simulation
Non-uniform mixing of quantum walk on cycles
arXiv
Authors: William Adamczak, Kevin Andrew, Leon Bergen, Dillon Ethier, Peter Hernberg, Jennifer Lin, Christino Tamon
Year
2007
Paper ID
49360
Status
Preprint
Abstract Read
~2 min
Abstract Words
94
Citations
N/A
Abstract
A classical lazy random walk on cycles is known to mix to the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibit strong non-uniform mixing properties. Our results include the following: - The instantaneous distribution of a quantum walk on most even-length cycles is never uniform. - The average distribution of a quantum walk on any Abelian circulant graph is never uniform. As a corollary, the average distribution of a quantum walk on any standard circulant graph, such as the cycles, complete graphs, and even hypercubes, is never uniform.
Why This Paper Matters
- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
- It adds a 2007 reference point for readers tracking recent quantum research.
- A classical lazy random walk on cycles is known to mix to the uniform distribution.
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