<p>Let us allow path to have same vertexes in it. (defining)</p>

<p>So suppose we have a graph of $N$ vertexes and we want to separate it into some superposition of paths that have $N$ vertexes (so if the number of vertexes is $N$, there would be like $N^N$ paths.)</p>

<p>Is this possible? If it is, how can this be done?</p>

CC BY-SA 3.0
2013-11-19T01:23:53.650Z
Create a uniform superposition over sufficiently many bits, and then use a classical algorithm to treat each outcome as the description of a path.
Mahdi Cheraghchi
CC BY-SA 3.0
2013-12-05T19:36:12.253Z
Some links that might be helpful: http://en.wikipedia.org/wiki/Continuous-time_quantum_walk ; http://arxiv.org/abs/quant-ph/0209131 ; http://prl.aps.org/abstract/PRL/v102/i18/e180501 ; http://arxiv.org/abs/1205.3782 and the references therein.
hadsed
<cc.complexity-theory><quantum-computing>
Quantum algorithm of graphs: How to create superposition of paths?
Qucomp
# Quantum algorithm of graphs: How to create superposition of paths?

(Asked by: username_0 on 2013-11-17)

Let us allow path to have same vertexes in it. (defining)

So suppose we have a graph of $N$ vertexes and we want to separate it into some superposition of paths that have $N$ vertexes (so if the number of vertexes is $N$, there would be like $N^N$ paths.)

Is this possible? If it is, how can this be done?

**Tags:** cc.complexity-theory, quantum-computing

> **Comments:**
> **username_1**: Create a uniform superposition over sufficiently many bits, and then use a classical algorithm to treat each outcome as the description of a path.  
> **username_2**: Some links that might be helpful: http://en.wikipedia.org/wiki/Continuous-time_quantum_walk ; http://arxiv.org/abs/quant-ph/0209131 ; http://prl.aps.org/abstract/PRL/v102/i18/e180501 ; http://arxiv.org/abs/1205.3782 and the references therein.  

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## 0 answers

