English

Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates

Quantum Physics 2015-07-14 v1

Abstract

Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for essentially any quantum control problem. So far this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here, using differential geometry, we reformulate the quantum brachistochrone curves as geodesics on the unitary group. With this identification we are able to obtain a numerical method that efficiently solves the brachistochrone problem. We apply it to two examples demonstrating its power.

Keywords

Cite

@article{arxiv.1408.2465,
  title  = {Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates},
  author = {Xiaoting Wang and Michele Allegra and Kurt Jacobs and Seth Lloyd and Cosmo Lupo and Masoud Mohseni},
  journal= {arXiv preprint arXiv:1408.2465},
  year   = {2015}
}

Comments

5 pages, 8 pages of supplemental material, 1 figure, 3 tables

R2 v1 2026-06-22T05:25:24.654Z