Abstract
We study quantum manipulation based on four Majorana bound states in X-junction geometry. The parameter space of this setup is bigger than of the previously studied Y-junction and is described by SO(4) symmetry group. In order for quantum computation to be dephasing free, two Majorana states have to stay degenerate at all times. We find a condition necessary for that and compute the Berry's phase, , accumulated during the manipulation. We construct simple protocols for the variety of values of α, including needed for the purposes of quantum computation. Although the manipulations in general X-junction geometry are not topologically protected, they may prove to be a feasible compromise for aims of quantum computation.
| Original language | English |
|---|---|
| Article number | 315301 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 49 |
| Issue number | 31 |
| DOIs | |
| State | Published - 28 Jun 2016 |
Bibliographical note
Publisher Copyright:© 2016 IOP Publishing Ltd.
Funding
We thank Yuval Oreg for useful discussions. This work was supported by the RFBR grant No15-52-06009 and by GIF (grant 1167-165.14/2011). DG acknowledges the support by ISF (grant 584/14) and the Israeli Ministry of Science.
| Funders | Funder number |
|---|---|
| Israeli Ministry of Science | |
| German-Israeli Foundation for Scientific Research and Development | 1167-165.14/2011 |
| Russian Foundation for Basic Research | |
| Israel Science Foundation | 584/14 |
Keywords
- Berry phase
- Majorana states
- X junction
- dephasing
- quantum computing
- topological protection