Searching nonadiabatic holonomic quantum gates via an optimization algorithm

Nonadiabatic holonomic quantum computation (NHQC) offers a way to realize geometric quantum gates beyond the adiabatic regime. To extend the flexibility and control robustness, many NHQC schemes have been proposed. Here, we propose to use quantum optimal control theory to search control sequences that can realize holonomic gates. Given a target gate and the corresponding computational subspace, our optimization algorithm can find the control sequence automatically. Furthermore, by defining an averaged target function, our method can improve the robustness of the holonomic gates against the errors such as thermal noises and amplitude errors. As an application, we search the control sequences for the Hadamard, not, and cnot gates in a nitrogen-vacancy-center system.