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Search algorithm on strongly regular graphs based on scattering quantum walk
| Content Provider | Scilit |
|---|---|
| Author | Xue, Xi-Ling Liu, Zhi-Hao Chen, Han-Wu |
| Copyright Year | 2017 |
| Description | Journal: Chinese Physics B Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs (SRGs) with parameters achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs. The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally. |
| Related Links | http://iopscience.iop.org/article/10.1088/1674-1056/26/1/010301/pdf |
| ISSN | 16741056 |
| e-ISSN | 20583834 |
| DOI | 10.1088/1674-1056/26/1/010301 |
| Journal | Chinese Physics B |
| Issue Number | 1 |
| Volume Number | 26 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 2017-01-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Chinese Physics B Quantum Walk Scattering Quantum Regular Graphs Strongly Regular Perturbation Theory Time Quantum |
| Content Type | Text |
| Resource Type | Article |
| Subject | Physics and Astronomy |
