https://github.com/iitis/comment-on-spatial-search
https://github.com/iitis/comment-on-spatial-search
Last synced: 3 months ago
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- Host: GitHub
- URL: https://github.com/iitis/comment-on-spatial-search
- Owner: iitis
- Created: 2020-09-28T11:44:04.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2020-09-28T13:00:38.000Z (over 5 years ago)
- Last Synced: 2025-03-17T17:59:36.513Z (about 1 year ago)
- Language: Julia
- Size: 3.91 KB
- Stars: 1
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Comment to *Spatial Search by Quantum Walk is Optimal for Almost all Graphs* (code)
Date: *28.09.2020*
Person responsible for data: *Adam Glos* (aglos [at] iitis.pl).
The scripts necessary for generating the plot presented in "Comment to Spatial Search by Quantum Walk is Optimal for Almost all Graphs".
## Used software
* Julia v1.3.1
* NPZ v0.4.0
* LightGraphs v1.3.3
* Expokit v0.2.0
* PyPlot v2.9.0
## Methodics
The calculations were based on the paper "Spatial Search by Quantum Walk is Optimal for Almost all Graphs" (doi.org/10.1103/PhysRevA.102.032214). For each graph order and each p=n^C, 10 Erdös-Renyi were sampled and the change of success probability calculated on the time interval [0, 2T]. Parameter T were calculated based on the proof of the Lemma in the referenced paper. The plots were done on a rescaled time axis, by dividing each time-point by 2T for each graph chosen. We chose the transition rates to be 1/(np) and the one proposed in the proof of the lemma.
To reconstruct the results, please run files therein:
```
julia single_case.jl
julia plotter.jl
```
The first line generates data which are stored in `data`. The latter command generates the plot.