dorsal/arxiv
View SchemaMixing in Continuous Quantum Walks on Graphs
| Authors | Amir Ahmadi, Ryan Belk, Christino Tamon, Carolyn Wendler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209106 |
| URL | https://arxiv.org/abs/quant-ph/0209106 |
| Journal | Quantum Information and Computation 3 (2003), 611-618. |
Abstract
Classical random walks on well-behaved graphs are rapidly mixing towards the uniform distribution. Moore and Russell showed that a continuous quantum walk on the hypercube is instantaneously uniform mixing. We show that the continuous-time quantum walks on other well-behaved graphs do not exhibit this uniform mixing. We prove that the only graphs amongst balanced complete multipartite graphs that have the instantaneous uniform mixing property are the complete graphs on two, three and four vertices, and the cycle graph on four vertices. Our proof exploits the circulant structure of these graphs. Furthermore, we conjecture that most complete cycles and Cayley graphs lack this mixing property as well.
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"abstract": "Classical random walks on well-behaved graphs are rapidly mixing towards the\nuniform distribution. Moore and Russell showed that a continuous quantum walk\non the hypercube is instantaneously uniform mixing. We show that the\ncontinuous-time quantum walks on other well-behaved graphs do not exhibit this\nuniform mixing. We prove that the only graphs amongst balanced complete\nmultipartite graphs that have the instantaneous uniform mixing property are the\ncomplete graphs on two, three and four vertices, and the cycle graph on four\nvertices. Our proof exploits the circulant structure of these graphs.\nFurthermore, we conjecture that most complete cycles and Cayley graphs lack\nthis mixing property as well.",
"arxiv_id": "quant-ph/0209106",
"authors": [
"Amir Ahmadi",
"Ryan Belk",
"Christino Tamon",
"Carolyn Wendler"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information and Computation 3 (2003), 611-618.",
"title": "Mixing in Continuous Quantum Walks on Graphs",
"url": "https://arxiv.org/abs/quant-ph/0209106"
},
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